Question 1

Solve the equation $$8^{x}$$ = $$4^{x-1}.$$

Accepted Answer

$$x = 2$$

Question 2

Give the domain and range of $$f(x) = \sqrt{x-1}.$$

Accepted Answer

Domain: $$[1, \infty)$$, Range: $$[0, \infty)$$

Question 3

Write $$3 \log x + \log y as a $$single logarithm.

Accepted Answer

$$\log(x^3$y)$$

Question 4

If $$1000 is $$invested at an annual interest rate of $$5\%$$ compounded quarterly, how long will it be until the amount doubles?

Accepted Answer

$$13.9$$ years

Question 5

Describe the effect on the graph of $$y = f(x) if$$ $$y = f(x+2) - 3 is $$formed as a sequence of transformations.

Accepted Answer

Shift left 2 units, then shift down 3 units

Question 6

Which of the following is the solution set for the quadratic equation $$x^2 - 3x - 28 = 0$?

Accepted Answer

$$x = 7, x = -4$$

Question 7

The points $$(1,1)$$, $$(4,1)$$, and $$(1,5)$$ form:

Accepted Answer

A right triangle

Question 8

Which equation is a quadratic equation in standard form?

Accepted Answer

$$x^2 + 2x - 7 = 0$

Question 9

The graph of $$y = (x-4)^2$ + 9 is$$:

Accepted Answer

A parabola with vertex $$(4,9)$$, opening upward

Question 10

Let $$f(x) = \begin{cases} x^2$ & x \u003c 0 \ x+1 & x \geq 0 \end{cases}. $$Which of the following statements is true?

Accepted Answer

$$f is $$discontinuous at $$x = 0$$

Question 11

Find the inverse function of $$f(x) = 2x + 3.$$

Accepted Answer

$$f^{-1}(x$$) = \frac{x-3}{2}$$

Question 12

Determine an equation for the exponential function whose graph passes through the points $$(0,5)$$ and $$(2,20).$$

Accepted Answer

$$y = 5 \cdot 2^x$$

Question 13

Determine the values of $$k$$ for which $$x^2 + 4x + k = 0$ will have exactly 2 real roots.

Accepted Answer

$$k \u003c 4$$

Question 14

Let $$f(x) = x^2$ and g(x) = x + 1$. Find (f$$ \circ g)(2)$$.

Accepted Answer

$$9$$

Question 15

If $$A = 2(1.05)^t$$ and $$A = 4$$ when $$t = x$$, what is the value of $$x$$?

Accepted Answer

$$\log_{1.05} 2$$

Question 16

The domain of $$\log_{b}(b^x - x) is$$:

Accepted Answer

$$0 \u003c x \u003c 1$$

Question 17

If $$f(x) = 4^x$$ then $$f(x+1) - f(x)$$ has graph:

Accepted Answer

An increasing exponential curve

Precalculus Standardized Test Preparation & Contest Problems: Study Notes

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