Question 1

Solve the equation $$7a(a-4) = 4a^2$ - 21a by $$factoring.

Accepted Answer

$$a = 0, -3/7$$

Question 2

Identify the x-intercepts of the function $$y = (x-3)^2$ - 9.$$

Accepted Answer

$$x = 0, 6$$

Question 3

Given that $$M$$ varies directly as $$O$$ and inversely as the cube root of $$N$$, which equation expresses $$N in $$terms of $$M$$ and $$O$$?

Accepted Answer

$$N = kO^3$/M^3$

Question 4

A brand-new laptop worth $$1000 has its value depreciating by 50$ per year. Which equation represents the value of the laptop, y$, in dollars, after x$ years?

Accepted Answer

$$y = 1000 - 50x$$

Question 5

For the function $$f(x) = 4(x+2)^2$ + 7(x+2) - 2$$, what are the x-intercepts?

Accepted Answer

$$x = -2.25, 0$$

Question 6

Determine the end behavior of the graph of the polynomial $$f(x) = -29x^4$ - 3x^2$ + 5x + 6.$$

Accepted Answer

Graph falls to the left and right

Question 7

Given $$f(x) = \log$$_{9}$$x$$ and $$g(x) = \ln(5x)$$, what is the domain of $$g(x)$$?

Accepted Answer

$$x \u003e 0$$

Question 8

Plot the function $$f(x) = (7/8)^x on $$the rectangular coordinate system. What is its end behavior as $$x 	o \infty$$?

Accepted Answer

$$f(x) 	o 0$$

Question 9

Use a calculator to approximate the value of $$e^{1.9} to $$four decimal places.

Accepted Answer

6.6858

Question 10

Verify if the equation $$n^2$$(\$$log_2 2^n$$) = $$n^3 is $$true. If not, provide the correct equation.

Accepted Answer

False, correct statement should be: $$n^2$$(\$$log_2 2^n$$) = $$n^2n$

Question 11

Determine the value of $$	an 30^\circ.$$

Accepted Answer

$$\dfrac{\sqrt{3}}{3}$$

Question 12

A wheel with a radius of $$2$$ meters spins at $$2$$ radians per second. What is the linear speed of a point on the edge of the wheel?

Accepted Answer

$$4 m/s$$

Question 13

Which of the following is the correct amplitude and period for the function $$y = 3\sin(x)$$?

Accepted Answer

Amplitude: $$3$$, Period: $$2\pi$$

Question 14

Solve the trigonometric equation $$\sin(2x) = 0$$ for $$x in $$the interval $$[0, 2\pi).$$

Accepted Answer

$$x = 0, \pi$$

Question 15

Given the function $$h(x) = \sqrt{2x-6}$$, what is its domain?

Accepted Answer

$$x \geq 3$$

Question 16

Which of the following is the correct transformation of $$f(x) = \sqrt{2x} to$$ $$h(x) = \sqrt{2x-6}$$?

Accepted Answer

Shift right by $$3$$ units

Question 17

If $$f(x) = \log_9$ x$$ and $$g(x) = \ln(5x)$$, what is the vertical asymptote of $$g(x)$$?

Accepted Answer

$$x = 0$$

Question 18

Use the half-angle formula to find the exact value of $$\sin(15^\circ).$$

Accepted Answer

$$\dfrac{\sqrt{6} - \sqrt{2}}{4}$$

Question 19

A chemical reaction's rate $$R is $$inversely proportional to the square of the concentration $$C. If$$ $$R = 5$$ when $$C = 2$$, what is $$R$$ when $$C = 5$$?

Accepted Answer

$$R = 0.8$$

Precalculus Study Guide: Functions, Graphs, and Algebraic Techniques

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