Question 1

Let $$L be $$the line $$y = 2x + 9. $$Let $$L' be $$the line through $$(-1, 6)$$ that is parallel to $$L. $$What is the equation of $$L'$$?

Accepted Answer

Question 2

Let $$L be $$the line $$y = 2x + 9. $$Let $$L' be $$the line through $$(-1, 6)$$ that is perpendicular to $$L. $$What is the equation of $$L'$$?

Accepted Answer

$$y = -\frac{1}{2}x + 5.5$$

Question 3

Find the average rate of change of $$f(x) = x^3$ + x + 1$$ from $$x = 2 to$$ $$x = 5.$$

Accepted Answer

$$49$$

Question 4

Find the $$x- $$and $$y-$$intercepts of the line $$4x + 5y = 7.$$

Accepted Answer

$$x-$$intercept: $$(\frac{7}{4}, 0)$$; $$y-$$intercept: $$(0, \frac{7}{5})$$

Question 5

Solve for $$w in $$the equation $$3h = 7c + 2w.$$

Accepted Answer

$$w = \frac{3h - 7c}{2}$$

Question 6

Let $$f(x) be $$the function graphed below (see image 4). Is $$f$$ continuous at $$x = 2$$?

Accepted Answer

No, because there is a jump discontinuity at $$x = 2.$$

Question 7

Is the function $$f(x) = x^2$ - 7x + 4$$ even, odd, or neither?

Accepted Answer

Neither

Question 8

Let $$f(x) = -3x^2$ + 2x. Is$$ $$f$$ even, odd, or neither?

Accepted Answer

Neither

Question 9

Let $$f(x) = |x|. Is$$ $$f$$ even, odd, or neither?

Accepted Answer

Even

Question 10

Let $$R be $$the graph of $$y = 7x^4$ + 5x^2$. Is R$ symmetric with respect to the y$-axis? Is R$ symmetric with respect to the origin?

Accepted Answer

Symmetric with respect to the $$y-$$axis, but not the origin.

Question 11

Describe the transformation from $$y = f(x) to$$ $$y = f(x + 3).$$

Accepted Answer

Shift the graph 3 units to the left.

Question 12

Describe the transformation from $$y = f(x) to$$ $$y = f(-x).$$

Accepted Answer

Reflect the graph across the $$y-$$axis.

Question 13

Solve the equation $$|3x - 5| + 4 = 1.$$

Accepted Answer

No solution

Question 14

Solve the inequality $$|5 - 2x| \u003e 10.$$

Accepted Answer

$$x  7.5$$

Question 15

Let $$f(x) = \frac{1}{x^4$}. Is$$ $$f$$ even, odd, or neither?

Accepted Answer

Even

Question 16

Given $$E = \left( \frac{r + d}{c} - g \right) b$$, solve for $$r.$$

Accepted Answer

Precalculus Study Guide: Lines, Functions, Symmetry, Transformations, and Equations

Study Guide - Practice Questions