Question 1

Find the domain of the function.
- y=10+$\frac { 10 } { 4 x + 12 }$

Accepted Answer

The answer of Find the domain of the function.
- y=10+\(\frac...

Question 2

The salary s of an employee in a given year y.

Accepted Answer

The answer of The salary s of an employee in...

Question 3

Decide whether or not the equation defines y as a function of x.
-$y = \frac { 6 } { x + 19 }$

Accepted Answer

For every value of x (except x = -19, where the denominator becomes 0), there is exactly one corresponding value of y. This satisfies the definition of a function.

Question 4

Suppose the cost of producing  x  objects was defined by the function $C ( x ) = \frac { 60 x } { \sqrt { 60 x - 10 } }$ What is the domain of the function defined by this equation?

Accepted Answer

The domain of the function is determined by the values of $x$ for which the function is defined. The denominator $\sqrt{60x - 10}$ must be greater than 0 to avoid division by zero and to keep the square root defined (since the square root of a negative number is not real). Setting $60x - 10 > 0$ gives $x > \frac{1}{6}$. Thus, the domain is all real numbers greater than $\frac{1}{6}$, which is $\left( \frac{1}{6}, \infty \right)$.

Question 5

Decide whether or not the equation defines y as a function of x.
-$y = 2 x - 3$

Accepted Answer

For every value of x, there is exactly one corresponding value of y, which satisfies the definition of a function.

Question 6

Decide whether or not the equation defines y as a function of x.
-$y = 2 x ^ { 2 } + 2 x - 1$

Accepted Answer

For every value of x, there is exactly one corresponding value of y, satisfying the definition of a function.

Question 7

Determine whether the given relationship defines a function. If so, identify the independent and dependent variable, and
why the relationship is a function.
-The balance b in a checking account on a given day x.

Accepted Answer

The answer of Determine whether the given relationship defines a...

Question 8

Determine whether the given relationship defines a function. If so, identify the independent and dependent variable, and
why the relationship is a function.
-Derek's weight w in second grade g.

Accepted Answer

The answer of Determine whether the given relationship defines a...

Question 9

A customer's savings account number n given the number of years y the account has been active.

Accepted Answer

A customer's savings account number is a unique identifier and does not change based on the number of years the account has been active.

Question 10

Decide whether or not the equation defines y as a function of x.
-$y ^ { 2 } = ( x - 6 ) ( x + 4 )$

Accepted Answer

The equation $y^2 = (x - 6)(x + 4)$ does not define y as a function of x because for some values of x, there can be two different values of y (positive and negative square roots), violating the definition of a function.

Question 11

Decide whether or not the equation defines y as a function of x.
-$x - y ^ { 2 } = - 8$

Accepted Answer

The answer of Decide whether or not the equation defines...

Question 12

Determine whether the given relationship defines a function. If so, identify the independent and dependent variable, and
why the relationship is a function.
-The temperature t on a backyard thermometer at 5 pm on a given day x.

Accepted Answer

The relationship defines a function because for each given day x (independent variable), there is exactly one temperature t (dependent variable) at 5 pm. This satisfies the definition of a function, where each input (day) has exactly one output (temperature).

Question 13

Decide whether or not the equation defines y as a function of x.
-$x ^ { 2 } + y = - 6$

Accepted Answer

The equation $x^2 + y = -6$ can be rearranged to $y = -x^2 - 6$, which defines y as a function of x because for each x-value, there is exactly one corresponding y-value.

Question 14

Determine whether the given relationship defines a function. If so, identify the independent and dependent variable, and
why the relationship is a function.
-Addy's height h on the first day d of school throughout elementary school.

Accepted Answer

For each day d (in this context, the first day of each school year), Addy has exactly one height h, satisfying the definition of a function where each input (independent variable d) has exactly one output (dependent variable h).

Question 15

Determine whether the given relationship defines a function. If so, identify the independent and dependent variable, and
why the relationship is a function.
-The temperature t on a backyard thermometer on a given day x.

Accepted Answer

The answer of Determine whether the given relationship defines a...

Question 16

The number of shares s of a certain stock traded on a given day x.

Accepted Answer

The statement "Yes; x, s; there is one number of shares s traded on any given day x." correctly identifies that for each given day x, there is a specific number of shares s traded, establishing a clear relationship between the day and the number of shares traded.

Question 17

This chart shows the fees for an 18-hole round of golf for each of the last 5 years at a local municipal golf course. Assume that this chart defines a function with the name of f. State the domain of f. $$\begin{array} { c | c } 
\text { Year } & \text { Fee } \
\hline 2008 & \$ 22 \
2009 & \$ 24 \
2010 & \$ 26 \
2011 & \$ 26 \
2012 & \$ 30
\end{array}$$

Accepted Answer

The domain of a function consists of all the first elements of the ordered pairs, which in this case are the years 2008, 2009, 2010, 2011, and 2012.

Question 18

Determine whether the given relationship defines a function. If so, identify the independent and dependent variable, and
why the relationship is a function.
-The salary s of an employee on her hiring date d.

Accepted Answer

The relationship defines a function because for each hiring date (independent variable d), there is exactly one salary (dependent variable s) associated with it. This satisfies the definition of a function, where each input (in this case, the hiring date) has exactly one output (the salary).

Question 19

Determine whether the given relationship defines a function. If so, identify the independent and dependent variable, and
why the relationship is a function.
-The balance in a checking account b at the close of business on a given day x.

Accepted Answer

The relationship defines a function because for each day x (independent variable), there is exactly one balance b (dependent variable) at the close of business. This satisfies the definition of a function, where each input (day) has exactly one output (balance).

Question 20

Decide whether or not the equation defines y as a function of x.
-$y = \sqrt { 3 x - 7 }$

Accepted Answer

The equation $y = \sqrt { 3 x - 7 }$ defines y as a function of x because for each x in the domain $x \geq \frac{7}{3}$, there is exactly one corresponding value of y. The square root function only outputs non-negative values, ensuring a single output for each valid input.

Quiz 1: Functions, Graphs, and Models; Linear Functions

Find the domain of the function. - y=10+ $\frac { 10 } { 4 x + 12 }$

The salary s of an employee in a given year y.

Decide whether or not the equation defines y as a function of x. - $y = \frac { 6 } { x + 19 }$

Suppose the cost of producing x objects was defined by the function $C ( x ) = \frac { 60 x } { \sqrt { 60 x - 10 } }$ What is the domain of the function defined by this equation?

Decide whether or not the equation defines y as a function of x. - $y = 2 x - 3$

Decide whether or not the equation defines y as a function of x. - $y = 2 x ^ { 2 } + 2 x - 1$

Determine whether the given relationship defines a function. If so, identify the independent and dependent variable, and why the relationship is a function. -The balance b in a checking account on a given day x.

Determine whether the given relationship defines a function. If so, identify the independent and dependent variable, and why the relationship is a function. -Derek's weight w in second grade g.

A customer's savings account number n given the number of years y the account has been active.

Decide whether or not the equation defines y as a function of x. - $y ^ { 2 } = ( x - 6 ) ( x + 4 )$

Decide whether or not the equation defines y as a function of x. - $x - y ^ { 2 } = - 8$

Determine whether the given relationship defines a function. If so, identify the independent and dependent variable, and why the relationship is a function. -The temperature t on a backyard thermometer at 5 pm on a given day x.

Decide whether or not the equation defines y as a function of x. - $x ^ { 2 } + y = - 6$

Determine whether the given relationship defines a function. If so, identify the independent and dependent variable, and why the relationship is a function. -Addy's height h on the first day d of school throughout elementary school.

Determine whether the given relationship defines a function. If so, identify the independent and dependent variable, and why the relationship is a function. -The temperature t on a backyard thermometer on a given day x.

The number of shares s of a certain stock traded on a given day x.

Determine whether the given relationship defines a function. If so, identify the independent and dependent variable, and why the relationship is a function. -The salary s of an employee on her hiring date d.

Determine whether the given relationship defines a function. If so, identify the independent and dependent variable, and why the relationship is a function. -The balance in a checking account b at the close of business on a given day x.

Decide whether or not the equation defines y as a function of x. - $y = \sqrt { 3 x - 7 }$

Quiz 1: Functions, Graphs, and Models; Linear Functions

Find the domain of the function. - y=10+ 104x+12\frac { 10 } { 4 x + 12 }4x+1210​

The salary s of an employee in a given year y.

Decide whether or not the equation defines y as a function of x. - y=6x+19y = \frac { 6 } { x + 19 }y=x+196​

Suppose the cost of producing x objects was defined by the function C(x) =60x60x−10C ( x ) = \frac { 60 x } { \sqrt { 60 x - 10 } }C(x) =60x−10​60x​ What is the domain of the function defined by this equation?

Decide whether or not the equation defines y as a function of x. - y=2x−3y = 2 x - 3y=2x−3

Decide whether or not the equation defines y as a function of x. - y=2x2+2x−1y = 2 x ^ { 2 } + 2 x - 1y=2x2+2x−1

Determine whether the given relationship defines a function. If so, identify the independent and dependent variable, and why the relationship is a function. -The balance b in a checking account on a given day x.

Determine whether the given relationship defines a function. If so, identify the independent and dependent variable, and why the relationship is a function. -Derek's weight w in second grade g.

A customer's savings account number n given the number of years y the account has been active.

Decide whether or not the equation defines y as a function of x. - y2=(x−6) (x+4) y ^ { 2 } = ( x - 6 ) ( x + 4 ) y2=(x−6) (x+4)

Decide whether or not the equation defines y as a function of x. - x−y2=−8x - y ^ { 2 } = - 8x−y2=−8

Determine whether the given relationship defines a function. If so, identify the independent and dependent variable, and why the relationship is a function. -The temperature t on a backyard thermometer at 5 pm on a given day x.

Decide whether or not the equation defines y as a function of x. - x2+y=−6x ^ { 2 } + y = - 6x2+y=−6

Determine whether the given relationship defines a function. If so, identify the independent and dependent variable, and why the relationship is a function. -Addy's height h on the first day d of school throughout elementary school.

Determine whether the given relationship defines a function. If so, identify the independent and dependent variable, and why the relationship is a function. -The temperature t on a backyard thermometer on a given day x.

The number of shares s of a certain stock traded on a given day x.

Determine whether the given relationship defines a function. If so, identify the independent and dependent variable, and why the relationship is a function. -The salary s of an employee on her hiring date d.

Determine whether the given relationship defines a function. If so, identify the independent and dependent variable, and why the relationship is a function. -The balance in a checking account b at the close of business on a given day x.

Decide whether or not the equation defines y as a function of x. - y=3x−7y = \sqrt { 3 x - 7 }y=3x−7​

Find the domain of the function. - y=10+ $\frac { 10 } { 4 x + 12 }$

Decide whether or not the equation defines y as a function of x. - $y = \frac { 6 } { x + 19 }$

Suppose the cost of producing x objects was defined by the function $C ( x ) = \frac { 60 x } { \sqrt { 60 x - 10 } }$ What is the domain of the function defined by this equation?

Decide whether or not the equation defines y as a function of x. - $y = 2 x - 3$

Decide whether or not the equation defines y as a function of x. - $y = 2 x ^ { 2 } + 2 x - 1$

Decide whether or not the equation defines y as a function of x. - $y ^ { 2 } = ( x - 6 ) ( x + 4 )$

Decide whether or not the equation defines y as a function of x. - $x - y ^ { 2 } = - 8$

Decide whether or not the equation defines y as a function of x. - $x ^ { 2 } + y = - 6$

Decide whether or not the equation defines y as a function of x. - $y = \sqrt { 3 x - 7 }$