Question 1

Given the graph below, what is the domain and range of the function $$y = f(x)$$?

Accepted Answer

Domain: $$[-4, 4]$$; Range: $$[-4, 4]$$

Question 2

For the function $$y = f(x)$$ shown in the first image, for what value of $$x is$$ $$f(x) = 5$$?

Accepted Answer

$$2$$

Question 3

Using the graph in the second image, what is the value of $$f at$$ $$x = 1$$?

Accepted Answer

$$4$$

Question 4

Which of the following is the correct plot for the point $$\left(-\frac{7}{2}, \frac{9}{2}\right)$$?

Accepted Answer

Image 5

Question 5

Determine the $$x- $$and $$y-$$intercepts of the graph shown in the last image.

Accepted Answer

$$x-$$intercepts: $$-2, 4$$; $$y-$$intercept: $$5$$

Question 6

A company tracks its profit over time and finds that the profit function $$P(x)$$ has a domain of $$[0, 4]. $$What does this mean in a real-world context?

Accepted Answer

The company can only make profits for $$x$$ values between $$0$$ and $$4.$$

Question 7

If a function $$f(x)$$ has a range of $$[-4, 4]$$, which of the following statements is true?

Accepted Answer

The function can take any $$y$$ value between $$-4$$ and $$4.$$

Question 8

Which of the following best describes the $$x-$$intercept of a function?

Accepted Answer

The point where $$y = 0.$$

Question 9

A medical researcher models the temperature of a patient over time with the function $$T(t). If $$the range of $$T is$$ $$[36, 40]$$, what does this mean?

Accepted Answer

The patient's temperature can be any value between $$36$$ and $$40$$ degrees.

Question 10

Suppose a function $$f(x) is $$defined only for $$x$$ values such that $$0 \u003c x \leq 4. $$Which of the following is the correct way to write the domain in set-builder notation?

Accepted Answer

$$\{x| 0 \u003c x \leq 4\}$$

Question 11

A chemical reaction is modeled by $$C(t)$$, where $$t is $$time in minutes. If $$C(3) = 5$$, what does this mean?

Accepted Answer

At $$t = 3$$ minutes, the concentration is $$5$$ units.

Question 12

Which of the following points is located at $$(-3.5, 4.5) on $$the Cartesian plane?

Accepted Answer

Image 6

Question 13

If a function $$f(x)$$ has $$x-$$intercepts at $$x = -2$$ and $$x = 4$$, and a $$y-$$intercept at $$y = 5$$, which of the following is true?

Accepted Answer

The graph crosses the $$x-$$axis at $$x = -2$$ and $$x = 4$$, and the $$y-$$axis at $$y = 5.$$

Graphs and Coordinates: College Algebra Study Guidance

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