Question 1

Determine whether or not the function is one-to-one.
-$\{(19,-5),(14,1),(1,10)\}$

Accepted Answer

Each element in the domain maps to a unique element in the range, so the function is one-to-one.

Question 2

Determine whether or not the function is one-to-one.
-$\{(-8,-18),(-17,-18),(-10,-4)\}$

Accepted Answer

A function is one-to-one if each x-value maps to a unique y-value. Here, both -8 and -17 map to -18, so it is not one-to-one.

Question 3

Determine whether or not the function is one-to-one.
-$\{(6,6),(7,6),(8,4),(9,-6)\}$

Accepted Answer

A function is one-to-one if each x-value maps to a unique y-value. In this set, both (6,6) and (7,6) map to the same y-value (6), so the function is not one-to-one.

Question 4

Determine whether or not the function is one-to-one.
-This chart shows the number of hits for five Little League baseball teams.

Accepted Answer

The answer of Determine whether or not the function is...

Question 5

Determine whether or not the function is one-to-one.
-This chart shows the number of living relatives in five families.

Accepted Answer

The answer of Determine whether or not the function is...

Question 6

Determine whether or not the function is one-to-one.
-The function that pairs the temperature in degrees Fahrenheit of a cup of coffee with its temperature in degrees Celsius.

Accepted Answer

The function that converts temperatures from Fahrenheit to Celsius is one-to-one because each temperature in Fahrenheit corresponds to exactly one temperature in Celsius, following the linear conversion formula $C = \frac{5}{9}(F - 32)$, where $F$ is the temperature in Fahrenheit and $C$ is the temperature in Celsius. This ensures a unique output (Celsius) for every unique input (Fahrenheit).

Question 7

Determine whether or not the function is one-to-one.
-The function that pairs the radius of a spherical bowling ball with its volume.

Accepted Answer

For each radius of a spherical bowling ball, there is exactly one volume associated with it, following the formula $V = \frac{4}{3}\pi r^3$, making the function one-to-one.

Question 8

Determine whether or not the function is one-to-one.
-$f(x)=2 x-4$

Accepted Answer

The function $f(x) = 2x - 4$ is one-to-one because for every unique input $x$, there is a unique output $f(x)$, and its slope (2) is not zero, indicating it passes the horizontal line test.

Question 9

Determine whether or not the function is one-to-one.
-$f(x)=x^{2}-5$

Accepted Answer

The function $f(x) = x^2 - 5$ is not one-to-one because different inputs can produce the same output. For example, $f(2) = 2^2 - 5 = -1$ and $f(-2) = (-2)^2 - 5 = -1$, so both $x = 2$ and $x = -2$ give the same result, violating the one-to-one criterion.

Question 10

Determine whether or not the function is one-to-one.
-$f(x)=3 x^{2}-5$

Accepted Answer

The function $f(x) = 3x^2 - 5$ is not one-to-one because it does not pass the horizontal line test; for any given y-value (except the vertex), there are two x-values that produce the same y-value, which violates the definition of a one-to-one function.

Question 11

Determine whether or not the function is one-to-one.
-$f(x)=x^{3}-1$

Accepted Answer

The function $f(x) = x^3 - 1$ is one-to-one because its derivative $f'(x) = 3x^2$ is always non-negative, and it only equals zero when $x = 0$, indicating that the function is strictly increasing or decreasing everywhere except possibly at a single point, thus passing the Horizontal Line Test for being one-to-one.

Question 12

Determine whether or not the function is one-to-one.
-$f(x)=\sqrt{4-x^{2}}$

Accepted Answer

The function $f(x)=\sqrt{4-x^{2}}$ is not one-to-one because for each y-value in the range, there are two different x-values (one positive and one negative) that produce the same y-value, violating the definition of a one-to-one function.

Question 13

Determine whether or not the function is one-to-one.
-

Accepted Answer

The answer of Determine whether or not the function is...

Question 14

Determine whether or not the function is one-to-one.
-

Accepted Answer

The answer of Determine whether or not the function is...

Question 15

If the following defines a one-to-one function, find its inverse. If not, write "Not one-to-one."
-$\{(9,-5),(13,6),(19,20)\}$
A) $\{(9,6),(9,13),(20,19)\}$
B) $\{(-5,9),(19,13),(20,6)\}$
C) $\{(-5,9),(6,13),(20,19)\}$
D) Not one-to-one

Accepted Answer

The function is one-to-one because each input has a unique output. The inverse is found by swapping the pairs, resulting in $\{(-5,9),(6,13),(20,19)\}$.

Question 16

If the following defines a one-to-one function, find its inverse. If not, write "Not one-to-one."
-$\{(-6,8),(-19,8),(-7,-12)\}$
A) $\{(-6,8),(8,-19),(-12,-7)\}$
B) $\{(8,-6),(-7,-19),(-12,8)\}$
C) Not one-to-one
D) $\{(8,-6),(8,-19),(-12,-7)\}$

Accepted Answer

The function is not one-to-one because it maps two different inputs (-6 and -19) to the same output (8).

Question 17

If the following defines a one-to-one function, find its inverse. If not, write "Not one-to-one."
-$\{(-2,4),(2,-4),(8,-2),(-8,2)\}$
A) $\{(4,-2),(-4,2),(-2,8),(2,-8)\}$
B) $\{(4,-2),(-4,2),(-2,-8),(2,8)\}$
C) Not one-to-one
D) $\{(4,-2),(-4,2),(8,-2),(2,-8)\}$

Accepted Answer

The given function is one-to-one because each domain value maps to a unique range value, and no range value is repeated. The inverse of a function swaps the positions of the elements in each ordered pair, making choice A the correct inverse.

Question 18

If the following defines a one-to-one function, find its inverse. If not, write "Not one-to-one."
-$\left\{\left(-3, \frac{1}{2}\right),(-2,-3),\left(-\frac{1}{3}, 2\right),\left(-9, \frac{3}{8}\right)\right\}$
A) $\left\{\left(\frac{1}{2}, 3\right),(-3,2),\left(2, \frac{1}{3}\right),\left(-\frac{3}{8},-9\right)\right\}$
B)$\left\{\left(\frac{1}{3},-3\right),(-3,-2),\left(2,-\frac{1}{2}\right),\left(\frac{3}{8},-9\right)\right\}$
C) Not one-to-one
D) $\left\{\left(\frac{1}{2},-3\right),(-3,-2),\left(2,-\frac{1}{3}\right),\left(\frac{3}{8},-9\right)\right\}$

Accepted Answer

The function is one-to-one because each input has a unique output. The inverse is found by swapping the x and y values in each pair.

Question 19

If the following defines a one-to-one function, find its inverse. If not, write "Not one-to-one."
-$f(x)=8 x^{2}-4$
A) Not one-to-one
B) $f^{-1}(x)=\sqrt{\frac{x+4}{8}}$
C) $f^{-1}(x)=\frac{x+4}{8}$
D) $f^{-1}(x)= \pm \sqrt{\frac{x+4}{8}}$

Accepted Answer

The function $f(x)=8x^2-4$ is not one-to-one because for any given y-value, there can be two different x-values (one positive and one negative) that produce the same y-value, violating the definition of a one-to-one function.

Question 20

If the following defines a one-to-one function, find its inverse. If not, write "Not one-to-one."
-$f(x)=x^{3}-5$
A) Not one-to-one
B) $f^{-1}(x)=x+5$
C) $f^{-1}(x)= \pm \sqrt[3]{x+5}$
D) $f^{-1}(x)=\sqrt[3]{x+5}$

Accepted Answer

The function $f(x)=x^{3}-5$ is one-to-one because for every x value, there is a unique y value, and its inverse can be found by solving for x: $y=x^{3}-5$ becomes $x=\sqrt[3]{y+5}$, so $f^{-1}(x)=\sqrt[3]{x+5}$.

Quiz 10: Inverse, Exponential, and Logarithmic Functions

Determine whether or not the function is one-to-one. - $\{(19,-5),(14,1),(1,10)\}$

Determine whether or not the function is one-to-one. - $\{(-8,-18),(-17,-18),(-10,-4)\}$

Determine whether or not the function is one-to-one. - $\{(6,6),(7,6),(8,4),(9,-6)\}$

Determine whether or not the function is one-to-one. -This chart shows the number of hits for five Little League baseball teams.

Determine whether or not the function is one-to-one. -This chart shows the number of living relatives in five families.

Determine whether or not the function is one-to-one. -The function that pairs the temperature in degrees Fahrenheit of a cup of coffee with its temperature in degrees Celsius.

Determine whether or not the function is one-to-one. -The function that pairs the radius of a spherical bowling ball with its volume.

Determine whether or not the function is one-to-one. - $f(x)=2 x-4$

Determine whether or not the function is one-to-one. - $f(x)=x^{2}-5$

Determine whether or not the function is one-to-one. - $f(x)=3 x^{2}-5$

Determine whether or not the function is one-to-one. - $f(x)=x^{3}-1$

Determine whether or not the function is one-to-one. - $f(x)=\sqrt{4-x^{2}}$

Determine whether or not the function is one-to-one. -

Determine whether or not the function is one-to-one. -

If the following defines a one-to-one function, find its inverse. If not, write "Not one-to-one." - $\{(9,-5) ,(13,6) ,(19,20) \}$

If the following defines a one-to-one function, find its inverse. If not, write "Not one-to-one." - $\{(-6,8) ,(-19,8) ,(-7,-12) \}$

If the following defines a one-to-one function, find its inverse. If not, write "Not one-to-one." - $\{(-2,4) ,(2,-4) ,(8,-2) ,(-8,2) \}$

If the following defines a one-to-one function, find its inverse. If not, write "Not one-to-one." - $\left\{\left(-3, \frac{1}{2}\right) ,(-2,-3) ,\left(-\frac{1}{3}, 2\right) ,\left(-9, \frac{3}{8}\right) \right\}$

If the following defines a one-to-one function, find its inverse. If not, write "Not one-to-one." - $f(x) =8 x^{2}-4$

If the following defines a one-to-one function, find its inverse. If not, write "Not one-to-one." - $f(x) =x^{3}-5$

Quiz 10: Inverse, Exponential, and Logarithmic Functions

Determine whether or not the function is one-to-one. - {(19,−5),(14,1),(1,10)}\{(19,-5),(14,1),(1,10)\}{(19,−5),(14,1),(1,10)}

Determine whether or not the function is one-to-one. - {(−8,−18),(−17,−18),(−10,−4)}\{(-8,-18),(-17,-18),(-10,-4)\}{(−8,−18),(−17,−18),(−10,−4)}

Determine whether or not the function is one-to-one. - {(6,6),(7,6),(8,4),(9,−6)}\{(6,6),(7,6),(8,4),(9,-6)\}{(6,6),(7,6),(8,4),(9,−6)}

Determine whether or not the function is one-to-one. -This chart shows the number of hits for five Little League baseball teams.

Determine whether or not the function is one-to-one. -This chart shows the number of living relatives in five families.

Determine whether or not the function is one-to-one. -The function that pairs the temperature in degrees Fahrenheit of a cup of coffee with its temperature in degrees Celsius.

Determine whether or not the function is one-to-one. -The function that pairs the radius of a spherical bowling ball with its volume.

Determine whether or not the function is one-to-one. - f(x)=2x−4f(x)=2 x-4f(x)=2x−4

Determine whether or not the function is one-to-one. - f(x)=x2−5f(x)=x^{2}-5f(x)=x2−5

Determine whether or not the function is one-to-one. - f(x)=3x2−5f(x)=3 x^{2}-5f(x)=3x2−5

Determine whether or not the function is one-to-one. - f(x)=x3−1f(x)=x^{3}-1f(x)=x3−1

Determine whether or not the function is one-to-one. - f(x)=4−x2f(x)=\sqrt{4-x^{2}}f(x)=4−x2​

Determine whether or not the function is one-to-one. -

Determine whether or not the function is one-to-one. -

If the following defines a one-to-one function, find its inverse. If not, write "Not one-to-one." - {(9,−5) ,(13,6) ,(19,20) }\{(9,-5) ,(13,6) ,(19,20) \}{(9,−5) ,(13,6) ,(19,20) }

If the following defines a one-to-one function, find its inverse. If not, write "Not one-to-one." - {(−6,8) ,(−19,8) ,(−7,−12) }\{(-6,8) ,(-19,8) ,(-7,-12) \}{(−6,8) ,(−19,8) ,(−7,−12) }

If the following defines a one-to-one function, find its inverse. If not, write "Not one-to-one." - {(−2,4) ,(2,−4) ,(8,−2) ,(−8,2) }\{(-2,4) ,(2,-4) ,(8,-2) ,(-8,2) \}{(−2,4) ,(2,−4) ,(8,−2) ,(−8,2) }

If the following defines a one-to-one function, find its inverse. If not, write "Not one-to-one." - f(x) =8x2−4f(x) =8 x^{2}-4f(x) =8x2−4

If the following defines a one-to-one function, find its inverse. If not, write "Not one-to-one." - f(x) =x3−5f(x) =x^{3}-5f(x) =x3−5

Determine whether or not the function is one-to-one. - $\{(19,-5),(14,1),(1,10)\}$

Determine whether or not the function is one-to-one. - $\{(-8,-18),(-17,-18),(-10,-4)\}$

Determine whether or not the function is one-to-one. - $\{(6,6),(7,6),(8,4),(9,-6)\}$

Determine whether or not the function is one-to-one. - $f(x)=2 x-4$

Determine whether or not the function is one-to-one. - $f(x)=x^{2}-5$

Determine whether or not the function is one-to-one. - $f(x)=3 x^{2}-5$

Determine whether or not the function is one-to-one. - $f(x)=x^{3}-1$

Determine whether or not the function is one-to-one. - $f(x)=\sqrt{4-x^{2}}$

If the following defines a one-to-one function, find its inverse. If not, write "Not one-to-one." - $\{(9,-5) ,(13,6) ,(19,20) \}$

If the following defines a one-to-one function, find its inverse. If not, write "Not one-to-one." - $\{(-6,8) ,(-19,8) ,(-7,-12) \}$

If the following defines a one-to-one function, find its inverse. If not, write "Not one-to-one." - $\{(-2,4) ,(2,-4) ,(8,-2) ,(-8,2) \}$

If the following defines a one-to-one function, find its inverse. If not, write "Not one-to-one." - $f(x) =8 x^{2}-4$

If the following defines a one-to-one function, find its inverse. If not, write "Not one-to-one." - $f(x) =x^{3}-5$