Question 1

Given the graph above, what is the value of $$f(3)$$?

Accepted Answer

$$f(3) = 3$$

Question 2

Let $$f(x) = -4x + 9$$ and $$g(x) = 8x^2$ + 7. $$Find $$(f-g)(3). $$

Accepted Answer

$$-52$$

Question 3

The MetroCity paint company has fixed costs of $$2500 and variable costs of 10$ per gallon. Each gallon sells for 40$. How many gallons must be sold to break even?

Accepted Answer

$$83$$

Question 4

Factor: $$14y^3$$ + $$63y^2 - 35y$

Accepted Answer

$$7y(2y^2 + 9y - 5$$)$$

Question 5

Without graphing, find the minimum value of $$f(x) = 2.75(x+4)^2$ - 10.$$

Accepted Answer

$$-10$$

Question 6

Evaluate $$6 - (a - b)^2$ when a = 13$ and b = 3$.

Accepted Answer

$$-94$$

Question 7

Find the equation of the line passing through $$(1.5, -5)$$ and $$(2.2, -1.6) in $$slope-intercept form.

Accepted Answer

$$y = 4.86x - 12.29$$

Question 8

Solve $$4x^2 - 6x = -1$ and write the answer using $$\pm$$ notation.

Accepted Answer

$$x = \frac{3 \pm \sqrt{13}}{4}$$

Question 9

Let $$f(x) = 7x - 2$$ and $$g(x) = 7x + 2. $$Find $$(f \cdot g)(x). $$

Accepted Answer

$$49x^2 - 4$

Question 10

Yearly sales of an electronic device are given by $$S(t) = 400 \cdot 2^t$$, where $$t is $$years after 1997. In what year did sales reach $$4,400$$ million?

Accepted Answer

$$2008$$

Question 11

What is the maximum product of two positive numbers whose sum is $$60$$?

Accepted Answer

$$900$$

Question 12

Simplify using the laws of exponents: $$\$$left(a^{\frac{3}$${5}} b$$^{-\frac{2}$${3}}\$$right)^{\frac{1}$${3}}$$

Accepted Answer

$$a^{\frac{1}$${5}} $$b^{-\frac{2}$${9}}$$

Question 13

Which of the following is a factor of $$36x^2 - 96x + 64$?

Accepted Answer

$$(6x - 8)$$

Question 14

A salesperson has two job offers. Company A: $$400$$ salary + $$10\%$$ commission. Company B: $$800$$ salary + $$5\%$$ commission. For what sales amount is Company A's offer better?

Accepted Answer

$$10,000$$

Question 15

Solve $$V = \frac{1}{3}Bh$$ for $$B.$$

Accepted Answer

$$B = \frac{3V}{h}$$

Question 16

Simplify $$\sqrt[3]{\frac{125x^7$}{y^8$z^{12}$$}}$, assuming all variables are positive.

Accepted Answer

$$\frac{5x^2$ \sqrt[3]{x}}{y$$^{2}$$z^{4}$$}$

Question 17

A projectile is thrown upward: $$H(t) = -13t^2$ + 520t. $$After how many seconds does it reach maximum height?

Accepted Answer

$$20$$

Question 18

Solve the inequality: $$9x - 6 \u003c 3x or$$ $$-2x \leq -6.$$

Accepted Answer

$$x \u003c 1 or$$ $$x \geq 3$$

Question 19

Rewrite $$a^x = 7 as an $$equivalent logarithmic equation.

Accepted Answer

$$x = \log_a 7$$

Question 20

Which of the following expressions is NOT equivalent to $$\ln\left(\frac{m^5$p^9$$}{$$n^4b^8$}\right)$$?

Accepted Answer

$$\ln m^5$ + 9\ln p - 4\ln n - 8\ln b$$

Intermediate Algebra Final Exam Review – Step-by-Step Guidance

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