Question 1

Which of the following is the correct domain for the function $$f(x) = \frac{1}{x-5}$$?

Accepted Answer

$$\{x \mid x 
eq 5\}$$

Question 2

Given the points $$(-7, -8)$$ and $$(7, -8)$$, what is the slope of the line passing through them?

Accepted Answer

$$m = 0$$

Question 3

If $$f(x) = x^2$ and g(x$$) = \sqrt{x+9}$$, what is (f$$ \circ g)(4)$$?

Accepted Answer

$$25$$

Question 4

Change the exponential equation $$e^x = 8 to $$logarithmic form.

Accepted Answer

$$x = \ln 8$$

Question 5

What is the solution set for $$x^2 = 16$?

Accepted Answer

$$x = 4, -4$$

Question 6

If $$f$$ denotes the inverse of a function $$f$$, then the graphs of $$f$$ and $$f^{-1}$$ are symmetric with respect to which line?

Accepted Answer

$$y = x$$

Question 7

What is the general form of the equation of a circle with center $$(h, k)$$ and radius $$r$$?

Accepted Answer

$$(x-h)^2$$ + $$(y-k)^2$$ = $$r^2$$

Question 8

Find the distance between the points $$P_1 = (0$$,0)$$ and P_2$ = (1,4).$$

Accepted Answer

$$\sqrt{17}$$

Question 9

Which of the following statements about the slope of a linear function is correct?

Accepted Answer

If the slope is positive, the function is increasing over its domain.

Question 10

What is the range of the function $$f(x) = x^2$?

Accepted Answer

$$[0, \infty)$$

Question 11

Which quadrant does the point $$(-4, -6)$$ lie in?

Accepted Answer

Quadrant III

Question 12

If $$f(x) = \ln x$$, what is the domain of $$f$$?

Accepted Answer

$$\{x \mid x \u003e 0\}$$

Question 13

Which of the following is the correct point-slope equation for a line with slope $$m$$ passing through $$(x_1$, y_1$)$$?

Accepted Answer

$$y - y_1$ = m(x - x_1$)$$

Question 14

Which of the following is the correct logarithmic property for $$\ln(ab)$$?

Accepted Answer

$$\ln(ab) = \ln a + \ln b$$

Question 15

If $$f(x) = x^2$ and g(x) = x+2$, what is (f$$ \circ g)(3)$$?

Accepted Answer

$$25$$

Question 16

What is the solution to $$\sqrt{x} = 5$$?

Accepted Answer

$$x = 25$$

Question 17

Which of the following is the correct property for $$\ln(a^b)$$?

Accepted Answer

$$\ln(a^b) = b \ln a$$

Question 18

If $$f(x) = x^2$ and g(x) = x+1$, what is (f$$ \circ g)(2)$$?

Accepted Answer

$$9$$

Question 19

Which of the following is the correct range for $$f(x) = \sqrt{x}$$?

Accepted Answer

$$[0, \infty)$$

Question 20

If $$f(x) = x^2$ and g(x) = x-3$, what is (f$$ \circ g)(5)$$?

Accepted Answer

$$4$$

Precalculus Study Guide: Functions, Graphs, Exponentials, Logarithms, and Geometry

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