Question 1

Given the points $$A(2, -3)$$ and $$B(-4, 5)$$, what is the distance between them?

Accepted Answer

$$\sqrt{(2 + 4)^2$ + (-3 - 5)^2$} = \sqrt{36 + 64} = \sqrt{100} = 10$$

Question 2

What is the midpoint between the points $$P(6, -2)$$ and $$Q(-2, 10)$$?

Accepted Answer

$$(2, 4)$$

Question 3

Which of the following equations represents a circle with center $$(3, -2)$$ and radius $$5$$?

Accepted Answer

$$(x - 3)^2$ + (y + 2)^2$ = 25$$

Question 4

Given the equation $$2x - 3y = 6$$, what are the $$x- $$and $$y-$$intercepts?

Accepted Answer

$$x-$$intercept: $$(3, 0)$$; $$y-$$intercept: $$(0, -2)$$

Question 5

Which of the following equations is symmetric with respect to the $$y-$$axis?

Accepted Answer

$$y = x^2$ + 1$$

Question 6

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

Accepted Answer

$$(-\infty, 4]$$

Question 7

Given $$f(x) = x^2$ - 3x + 2$$, compute the difference quotient $$\dfrac{f(x+h) - f(x)}{h}.$$

Accepted Answer

$$2x + h - 3$$

Question 8

Which of the following sets represents a function?

Accepted Answer

$$\{(1,2), (2,3), (3,4)\}$$

Question 9

If $$f(x) = 2x + 1$$ and $$g(x) = x^2$, what is (f + g)(3$$)$$?

Accepted Answer

$$2 \cdot 3 + 1 + 3^2$ = 6 + 1 + 9 = 16$$

Question 10

Given the line passing through $$(1, 2)$$ with slope $$-3$$, what is its equation in point-slope form?

Accepted Answer

$$y - 2 = -3(x - 1)$$

Question 11

Which of the following pairs of lines are perpendicular?

Accepted Answer

$$y = 2x + 1$$ and $$y = -\dfrac{1}{2}x + 3$$

Question 12

Given $$f(x) = x^3$, determine if f$ is even, odd, or neither.

Accepted Answer

Odd

Question 13

A circle has the equation $$x^2$$ + $$y^2 - 6x + 8y = 0$. What is its center and radius?

Accepted Answer

Center: $$(3, -4)$$, Radius: $$5$$

Question 14

If $$f(x) = x^2$ and g(x) = x + 1$, what is the domain of $$\dfrac{f}{g}$$?

Accepted Answer

$$x 
eq -1$$

Question 15

Find the average rate of change of $$f(x) = x^2$ from x = 1$ to x = 4$.

Accepted Answer

$$\dfrac{f(4) - f(1)}{4 - 1} = \dfrac{16 - 1}{3} = 5$$

Question 16

Given $$f(x) = |x|$$, which statement is true about its symmetry?

Accepted Answer

$$f is $$even

Question 17

Given $$f(x) = x^2$ - 4$$ and $$g(x) = x - 2$$, find $$(f \circ g)(3).$$

Accepted Answer

$$f(g(3)) = f(1) = 1 - 4 = -3$$

Question 18

A company’s profit $$P(x) (in $$thousands of dollars) is modeled by $$P(x) = -2x^2$ + 8x + 10$$, where $$x is $$the number of units sold (in thousands). For what value of $$x$$ does the profit reach its maximum?

Accepted Answer

$$x = 2$$

Question 19

Given the points $$A(1, 2)$$ and $$B(4, 10)$$, what is the equation of the secant line passing through $$A$$ and $$B$$?

Accepted Answer

$$y - 2 = \dfrac{10 - 2}{4 - 1}(x - 1)$$

Precalculus Study Guide test 1: Graphs, Lines, Circles, and Functions (Sections 1.1–1.4, B3/B4, 2.1–2.3)

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