Q: Given $$f(x) = 5x - 7$$ and $$g(x) = 3x - 2$$, find $$(f-g)(x)$$ and its domain.

$$(f-g)(x) = 2x - 5;\ \text{all real numbers}$$

Question 1

Find $$f(-3)$$ for the function $$f(x) = x^2$ - 5x + 7.$$

Accepted Answer

$$31$$

Question 2

What is the domain of the function $$f(x) = \dfrac{x}{x^2$ + 10}$$?

Accepted Answer

$$	ext{all real numbers}$$

Question 3

Given $$f(x) = 5x - 7$$ and $$g(x) = 3x - 2$$, find $$(f-g)(x)$$ and its domain.

Accepted Answer

$$(f-g)(x) = 2x - 5;\ 	ext{all real numbers}$$

Question 4

Consider the graph shown in the first image. Is this the graph of a function? If so, what is its domain, range, intercepts, and symmetry?

Accepted Answer

Function; domain: $$\{x \mid -\pi \leq x \leq \pi\}$$; range: $$\{y \mid -1 \leq y \leq 1\}$$; intercepts: $$(-\pi, 0), (0, 0), (\pi, 0)$$; symmetry: origin

Question 5

For the graph shown in the second image, for what values of $$x is$$ $$f(x) = 0$$?

Accepted Answer

$$-6, 7, 10$$

Question 6

Given $$f(x) = 3x^2$ - 6x - 2$$, is the point $$(2, 4) on $$the graph of $$f$$?

Accepted Answer

No

Question 7

Determine algebraically whether the function $$f(x) = 5x^2$ + 9 is $$even, odd, or neither.

Accepted Answer

Even

Question 8

For the graph shown in the third image, at what $$x-$$values does $$f$$ have a local maximum, and what are the local maxima?

Accepted Answer

$$f$$ has a local maximum at $$x = 0$$; the local maximum is $$2$$

Question 9

Find the average rate of change for $$f(x) = x^2$ + 3x$$ from $$x = 6 to$$ $$x = 8.$$

Accepted Answer

$$17$$

Question 10

Which of the following graphs (images 4-7) best represents the function $$f(x) = x$$?

Accepted Answer

Image 7

Question 11

Locate any intercepts of the piecewise function:

$$f(x) = \begin{cases} 1 & 	ext{if } -2 \leq x \u003c -4 \ |x| & 	ext{if } -4 \leq x \u003c 2 \ x & 	ext{if } 2 \leq x \leq 16 \end{cases}$$

Accepted Answer

$$(0, 0)$$

Question 12

Which function matches the graph shown in image 8?

Accepted Answer

$$y = x - 1$$

Question 13

Graph the function $$f(x) = (x-3)^2$ + 6 by $$starting with the graph of the basic function and using shifting, compressing, stretching, and/or reflecting. Which image (9-12) matches?

Accepted Answer

Image 10

Question 14

Given the graph of $$y = f(x)$$, which image (13-16) best represents the graph of $$y = -\frac{1}{2}f(x)$$?

Accepted Answer

Image 16

Question 15

Graph the function $$f(x) = -(x-6)^2$ + 5 by $$starting with the graph of the basic function and using shifting, compressing, stretching, and/or reflecting. Which image (17-20) matches?

Accepted Answer

Image 19

Question 16

A company models its profit with the function $$P(x) = -2x^2$ + 8x + 10$$, where $$x is $$the number of units sold (in thousands). What is the maximum profit, and for how many units sold does it occur?

Accepted Answer

Maximum profit is $$18 at$$ $$x = 2$$ thousand units

Question 17

Suppose $$f(x) is an $$even function and $$f(3) = 7. $$What is $$f(-3)$$?

Accepted Answer

$$7$$

Question 18

If $$g(x) = \sqrt{x-4}$$, what is the domain of $$g$$?

Accepted Answer

$$\{x \mid x \geq 4\}$$

Question 19

A medication's concentration in the bloodstream is modeled by $$C(t) = 20e$$^{-0.5t}$$, where t$ is in hours. What is the concentration after 3$ hours?

Accepted Answer

$$20e^{-1.5}$$

Question 20

Which of the following statements is true about the function $$h(x) = \dfrac{1}{x-2}$$?

Accepted Answer

The domain is all real numbers except $$x = 2$$

Precalculus Exam 1 Review – Step-by-Step Guidance

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