Question 1

Which of the following statements about the definition of a function is correct?

Accepted Answer

A function assigns each input to exactly one output.

Question 2

Given the function $$f(x) = x^2$ + 1$$, what is the domain $$D$$ and range $$R of$$ $$f$$?

Accepted Answer

$$D = \{x \in \mathbb{R}\}, R = \{y \in \mathbb{R} : y \geq 1\}$$

Question 3

Suppose $$g(3) = 4$$ and $$g(-3) = 4. Is$$ $$g a $$function?

Accepted Answer

Yes, because each input has exactly one output.

Question 4

Which of the following graphs pass the vertical line test and could represent a function?

Accepted Answer

A and C

Question 5

Find the domain of the function $$f(x) = \sqrt{x - 5}.$$

Accepted Answer

$$x \geq 5$$

Question 6

Let $$f be $$defined by $$f(2) = 1$$ and $$g(x) = x^2$ - 3. $$What is $$(g \circ f)(2)$$?

Accepted Answer

5

Question 7

Which of the following is the correct piecewise definition of the absolute value function $$f(x) = |x|$$?

Accepted Answer

$$f(x) = x$$ for $$x \geq 0$$, $$f(x) = -x$$ for $$x \u003c 0$$

Question 8

A study finds that the likelihood of kidney disease in a certain dog breed is best modeled by a linear function of weight. If the model predicts 10 cases per 1000 dogs at 10 kg and 30 cases per 1000 dogs at 30 kg, what is the equation of the model?

Accepted Answer

Question 9

A study finds that the likelihood of kidney disease in a certain dog breed is best modeled by a linear function of weight. If the model predicts 10 cases per 1000 dogs at 10 kg and 30 cases per 1000 dogs at 30 kg, what is the equation of the model?

Accepted Answer

Question 10

If $$f(x) = 2x + 3$$, which transformation describes $$g(x) = f(x - 4) + 1$$?

Accepted Answer

Shift right by 4, shift up by 1

Question 11

Which of the following is NOT a transformation effect you can apply to a function $$f(x)$$?

Accepted Answer

Rotation about the origin

Question 12

Which of the following statements about inverse functions is TRUE?

Accepted Answer

A function has an inverse if and only if it is one-to-one.

Question 13

Given $$f(x) = 3x + 5$$, what is the inverse function $$f^{-1}(x$$)$$?

Accepted Answer

$$f^{-1}(x$$) = \frac{x - 5}{3}$$

Question 14

Suppose the concentration of air pollution $$P (in $$ppm) at a distance $$x (in $$meters) from a highway is given by a decreasing function. If $$P(100) = 200$$, what does $$P^{-1}(100$$)$$ represent?

Accepted Answer

The distance from the highway where the pollution is 100 ppm

Question 15

If $$f(x) is an $$even function, which of the following must be true for all $$x in $$the domain of $$f$$?

Accepted Answer

$$f(-x) = f(x)$$

Question 16

Which of the following is a correct method to find the inverse of a function $$y = f(x)$$?

Accepted Answer

Switch $$x$$ and $$y$$, then solve for $$y$$

Question 17

A function $$f is $$defined as $$f(x) = x^2$ - 4x + 3. $$For which values of $$x$$ does $$f(x) = 0$$?

Accepted Answer

$$x = 1$$ and $$x = 3$$

Question 18

If $$f(x) is $$invertible, which of the following must be true?

Accepted Answer

The graph of $$f(x)$$ passes the horizontal line test.

Question 19

Suppose $$f(x) = x^2$ and g(x) = x + 1$. What is (f$$ \circ g)(2)$$?

Accepted Answer

9

Question 20

A daycare must be at least $$d$$ meters from a highway so that air pollution does not exceed 50 ppm. If $$P(x) is a $$decreasing function and $$P^{-1}(50) = 300$, what does this mean?

Accepted Answer

The pollution is 50 ppm at 300 meters from the highway.

MAT135 – Differential Calculus: Functions and Graphs Study Notes

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