Question 1

Determine whether the equation defines y as a function of x.
-$$y = | x |$$
A) function
B) not a function

Accepted Answer

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

Question 2

Determine whether the equation defines y as a function of x.
-$$y ^ { 2 } + x = 5$$
A) function
B) not a function

Accepted Answer

For an equation to define y as a function of x, each x-value must correspond to exactly one y-value. In the given equation, $y^2 + x = 5$, solving for y gives $y = \pm \sqrt{5 - x}$. This means for each x-value, there are two possible y-values (one positive and one negative), violating the definition of a function. Therefore, it does not define y as a function of x.

Question 3

Find the value for the function.
-Find f( $( x - 1 ) \text { when } f ( x ) = 2 x ^ { 2 } - 2 x + 2$ 
A) $2 x ^ { 2 } + 2 x + 2$
B) $2 x ^ { 2 } - 6 x + 2$
C) $- 6 x ^ { 2 } + 2 x + 6$
D) $2 x ^ { 2 } - 6 x + 6$

Accepted Answer

To find $f(x-1)$, substitute $x-1$ for $x$ in the given function $f(x) = 2x^2 - 2x + 2$. This gives $f(x-1) = 2(x-1)^2 - 2(x-1) + 2$. Expanding and simplifying, $f(x-1) = 2(x^2 - 2x + 1) - 2x + 2 + 2 = 2x^2 - 4x + 2 - 2x + 4 = 2x^2 - 6x + 6$.

Question 4

Determine whether the equation defines y as a function of x.
-$$y = \frac { 3 x - 4 } { x - 2 }$$
A) function
B) not a function

Accepted Answer

The equation defines y as a function of x because for each value of x (except x = 2, where the function is undefined due to division by zero), there is exactly one corresponding value of y.

Question 5

Determine whether the equation defines y as a function of x.
-$$x + 8 y = 4$$
A) function
B) not a function

Accepted Answer

This equation can be rearranged to solve for y in terms of x, making y a function of x.

Question 6

Find the value for the function.
-$$\text { Find } f ( 1 ) \text { when } f ( x ) = x ^ { 2 } - 5 x - 2$$
A) -6
B) 8
C) -2
D) 4

Accepted Answer

Substituting $x = 1$ into the function $f(x) = x^2 - 5x - 2$, we get $f(1) = 1^2 - 5(1) - 2 = 1 - 5 - 2 = -6$.

Question 7

Determine whether the equation defines y as a function of x.
-$$y ^ { 2 } = 5 - x ^ { 2 }$$
A) function
B) not a function

Accepted Answer

The equation does not define y as a function of x because for a given x-value, there can be two different y-values (one positive and one negative) that satisfy the equation, violating the definition of a function where each input should have exactly one output.

Question 8

Determine whether the equation defines y as a function of x. -y = x² A) function B) not a function

Accepted Answer

The equation y = x^2 defines y as a function of x because for each value of x, there is exactly one corresponding value of y. This satisfies the definition of a function.

Question 9

Find the value for the function. -Find -f(x) when f(x) = -2x² - 5x + 2. A) $2 x ^ { 2 } + 5 x + 2$ B) $- 2 x ^ { 2 } + 5 x + 2$ C) $- 2 x ^ { 2 } + 5 x - 2$ D) $2 x ^ { 2 } + 5 x - 2$

Accepted Answer

The answer of Find the value for the function.
-Find -f(x)...

Question 10

Find the value for the function.
-Find -f(x) when f(x) = |x| + 1. 
A) $| - x | - 1$
B) $- | x | - 1$
C) $- | x | + 1$
D) $| - x | + 1$

Accepted Answer

The function -f(x) applies a negative sign to the entire original function f(x) = |x| + 1, resulting in -(|x| + 1) = -|x| - 1.

Question 11

Determine whether the equation defines y as a function of x.
-$$x = y ^ { 2 }$$
A) function
B) not a function

Accepted Answer

For a given value of x, there can be two values of y (one positive and one negative) because squaring either gives the same result. This violates the definition of a function, which requires each input to have exactly one output.

Question 12

Determine whether the equation defines y as a function of x.
-$$- 7 x + x ^ { 2 } + 35 = y$$
A) function
B) not a function

Accepted Answer

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

Question 13

Find the value for the function.
-$$\text { Find } f ( - 9 ) \text { when } f ( x ) = | x | - 6$$
A) 15
B) -3
C) -15
D) 3

Accepted Answer

The answer of Find the value for the function.
-\[\text {...

Question 14

Find the value for the function.
-$\text { Find } f ( 8 ) \text { when } f ( x ) = \sqrt { x ^ { 2 } + 6 x }$ 
A) $4 \sqrt { 7 }$
B) $\sqrt { 42 }$
C) $\sqrt { 70 }$
D) 10

Accepted Answer

The answer of Find the value for the function.
-\(\text {...

Question 15

Determine whether the equation defines y as a function of x.
-$$x ^ { 2 } - 4 y ^ { 2 } = 1$$
A) function
B) not a function

Accepted Answer

For an equation to define y as a function of x, each x-value must correspond to exactly one y-value. The given equation $x^2 - 4y^2 = 1$ can be rearranged to $4y^2 = x^2 - 1$, and then $y^2 = \frac{x^2 - 1}{4}$. This shows that for a given x-value (except for x = 1 or x = -1), there are two corresponding y-values (one positive and one negative), which violates the definition of a function. Therefore, the equation does not define y as a function of x.

Question 16

Find the value for the function.
-$\text { Find } f ( - x ) \text { when } f ( x ) = 3 x ^ { 2 } - 4 x + 5$ 
A) $- 3 x ^ { 2 } + 4 x - 5$
B) $- 3 x ^ { 2 } + 4 x + 5$
C) $3 x ^ { 2 } + 4 x - 5$
D) $3 x ^ { 2 } + 4 x + 5$

Accepted Answer

The answer of Find the value for the function.
-\(\text {...

Question 17

Determine whether the equation defines y as a function of x.
-$$y = \frac { 1 } { x }$$
A) function
B) not a function

Accepted Answer

The equation $y = \frac{1}{x}$ defines y as a function of x because for each value of x (except x = 0), there is exactly one corresponding value of y.

Question 18

Determine whether the equation defines y as a function of x.
-$$y = 2 x ^ { 2 } - 5 x + 9$$
A) function
B) not a function

Accepted Answer

The equation $y = 2x^2 - 5x + 9$ is a polynomial of degree 2, which means for every value of $x$, there is exactly one corresponding value of $y$. This satisfies the definition of a function.

Question 19

Find the value for the function.
-$( - x ) \text { when } f ( x ) = \frac { x } { x ^ { 2 } + 1 }$ 
A) $\frac { - x } { x ^ { 2 } + 1 }$
B) $\frac { - x } { - x ^ { 2 } + 1 }$
C) $\frac { x } { - x ^ { 2 } + 1 }$
D) $\frac { - x } { x ^ { 2 } - 1 }$

Accepted Answer

The function $f(x) = \frac{x}{x^2 + 1}$ when evaluated at $-x$ becomes $\frac{-x}{(-x)^2 + 1} = \frac{-x}{x^2 + 1}$, which matches option A.

Question 20

Determine whether the equation defines y as a function of x.
-$$y = \pm \sqrt { 1 - 6 x }$$
A) function
B) not a function

Accepted Answer

The equation does not define y as a function of x because for each x value, there are two possible y values (due to the ± sign), which violates the definition of a function where each input should have exactly one output.

Quiz 1: Functions and Their Graphs

Determine whether the equation defines y as a function of x. - $y = | x |$

Determine whether the equation defines y as a function of x. - $y ^ { 2 } + x = 5$

Find the value for the function. -Find f( $( x - 1 ) \text { when } f ( x ) = 2 x ^ { 2 } - 2 x + 2$

Determine whether the equation defines y as a function of x. - $y = \frac { 3 x - 4 } { x - 2 }$

Determine whether the equation defines y as a function of x. - $x + 8 y = 4$

Find the value for the function. - $\text { Find } f ( 1 ) \text { when } f ( x ) = x ^ { 2 } - 5 x - 2$

Determine whether the equation defines y as a function of x. - $y ^ { 2 } = 5 - x ^ { 2 }$

Determine whether the equation defines y as a function of x. -y = x²

Find the value for the function. -Find -f(x) when f(x) = -2x² - 5x + 2.

Find the value for the function. -Find -f(x) when f(x) = |x| + 1.

Determine whether the equation defines y as a function of x. - $x = y ^ { 2 }$

Determine whether the equation defines y as a function of x. - $- 7 x + x ^ { 2 } + 35 = y$

Find the value for the function. - $\text { Find } f ( - 9 ) \text { when } f ( x ) = | x | - 6$

Find the value for the function. - $\text { Find } f ( 8 ) \text { when } f ( x ) = \sqrt { x ^ { 2 } + 6 x }$

Determine whether the equation defines y as a function of x. - $x ^ { 2 } - 4 y ^ { 2 } = 1$

Find the value for the function. - $\text { Find } f ( - x ) \text { when } f ( x ) = 3 x ^ { 2 } - 4 x + 5$

Determine whether the equation defines y as a function of x. - $y = \frac { 1 } { x }$

Determine whether the equation defines y as a function of x. - $y = 2 x ^ { 2 } - 5 x + 9$

Find the value for the function. - $( - x ) \text { when } f ( x ) = \frac { x } { x ^ { 2 } + 1 }$

Determine whether the equation defines y as a function of x. - $y = \pm \sqrt { 1 - 6 x }$

Quiz 1: Functions and Their Graphs

Determine whether the equation defines y as a function of x. - y=∣x∣y = | x |y=∣x∣

Determine whether the equation defines y as a function of x. - y2+x=5y ^ { 2 } + x = 5y2+x=5

Find the value for the function. -Find f( (x−1) when f(x) =2x2−2x+2( x - 1 ) \text { when } f ( x ) = 2 x ^ { 2 } - 2 x + 2(x−1) when f(x) =2x2−2x+2

Determine whether the equation defines y as a function of x. - y=3x−4x−2y = \frac { 3 x - 4 } { x - 2 }y=x−23x−4​

Determine whether the equation defines y as a function of x. - x+8y=4x + 8 y = 4x+8y=4

Find the value for the function. - Find f(1) when f(x) =x2−5x−2\text { Find } f ( 1 ) \text { when } f ( x ) = x ^ { 2 } - 5 x - 2 Find f(1) when f(x) =x2−5x−2

Determine whether the equation defines y as a function of x. - y2=5−x2y ^ { 2 } = 5 - x ^ { 2 }y2=5−x2

Determine whether the equation defines y as a function of x. -y = x2

Find the value for the function. -Find -f(x) when f(x) = -2x2 - 5x + 2.

Find the value for the function. -Find -f(x) when f(x) = |x| + 1.

Determine whether the equation defines y as a function of x. - x=y2x = y ^ { 2 }x=y2

Determine whether the equation defines y as a function of x. - −7x+x2+35=y- 7 x + x ^ { 2 } + 35 = y−7x+x2+35=y

Find the value for the function. - Find f(−9) when f(x) =∣x∣−6\text { Find } f ( - 9 ) \text { when } f ( x ) = | x | - 6 Find f(−9) when f(x) =∣x∣−6

Find the value for the function. - Find f(8) when f(x) =x2+6x\text { Find } f ( 8 ) \text { when } f ( x ) = \sqrt { x ^ { 2 } + 6 x } Find f(8) when f(x) =x2+6x​

Determine whether the equation defines y as a function of x. - x2−4y2=1x ^ { 2 } - 4 y ^ { 2 } = 1x2−4y2=1

Find the value for the function. - Find f(−x) when f(x) =3x2−4x+5\text { Find } f ( - x ) \text { when } f ( x ) = 3 x ^ { 2 } - 4 x + 5 Find f(−x) when f(x) =3x2−4x+5

Determine whether the equation defines y as a function of x. - y=1xy = \frac { 1 } { x }y=x1​

Determine whether the equation defines y as a function of x. - y=2x2−5x+9y = 2 x ^ { 2 } - 5 x + 9y=2x2−5x+9

Find the value for the function. - (−x) when f(x) =xx2+1( - x ) \text { when } f ( x ) = \frac { x } { x ^ { 2 } + 1 }(−x) when f(x) =x2+1x​

Determine whether the equation defines y as a function of x. - y=±1−6xy = \pm \sqrt { 1 - 6 x }y=±1−6x​