Practice Test 5 - College Algebra

20 questions. Answer them in any order, then submit to see your score and every explanation.

A bookstore tracks monthly profit (USD): month 1: 1400, month 2: 1550, month 3: 1700, month 4: 1850, month 5: 2000. A linear model is used to predict profits for ordering stock. Let $x$ be month number and $y$ be profit. What does the slope represent in this context?
Solve for $x$ and check for extraneous solutions: $\sqrt{4x}=10.$
How can the change of base formula be used to rewrite $\log_{1/2}(8)$ in terms of common logarithms?
A student is solving the equation $\frac{2x-1}{3} - \frac{x+4}{6} = \frac{x-2}{2}$ . After finding a common denominator and combining fractions, what is the resulting equation before solving for $x$ ?
After simplifying $\frac{x^2 + 5x + 6}{x^2 - x - 6}$ , what is the domain of the resulting expression?
The cost of producing $x$ items follows the linear function $C(x) = 15x + 200$ . A competing company has a cost function with the same fixed costs but a marginal cost that is $3 higher per item. What is the slope of the competing company's cost function?
Consider the system of equations: $3x - 2y = 7$ and $x + 4y = -1$ . When solving by substitution, if you solve the second equation for $x$ and substitute into the first equation, what equation in terms of $y$ do you obtain?
Which of the following correctly applies the product rule to $\log_b(xy)$ ?
A student solving $7x + 4y = 26$ and $5x - 3y = 13$ by elimination makes an error and gets the solution $(2, 3)$ . When checking this solution in the original equations, what will they discover?
A function $f(x)$ passes through the points $(-3, 7)$ and $(5, -1)$ . If $g(x) = f(x - 2) + 3$ , what is the average rate of change of $g(x)$ over the interval $[-1, 7]$ ?
How does rationalizing the denominator of $\frac{1}{4+\sqrt{2}}$ change it to a single fraction? Give your answer in simplest form.
Which of the following correctly identifies the property that allows us to conclude that if $x + 5 = 12$ , then $x + 5 + (-5) = 12 + (-5)$ ?
A relation $R$ is defined by the set of ordered pairs $\{(2, 3), (4, 5), (2, 7), (6, 9), (8, 5)\}$ . Which statement best describes why this relation fails to be a function?
Given that $a = 2^x$ and $b = 3^x$ , express $6^x + 6^{x+1}$ in terms of $a$ and $b$ .
Which shows $30x^2-45x$ factored completely by its GCF?
A savings account uses $A(t)=2500(1.05)^t$ ; what happens if the initial amount is doubled?
An account grows by 7% yearly from $P$ ; which base correctly represents the growth factor?
Consider the polynomial function $f(x) = (x + 2)^3(x - 1)^2(x - 4)$ . Which statement best describes the behavior of the graph at $x = -2$ ?
The graph of $y = f(x)$ passes through the point $(3, -2)$ . After applying the transformation $y = 2f(x-1) + 3$ , through which point does the new graph pass?
The equation $kx^2 + 8x + k = 0$ has real solutions when the discriminant is non-negative. For which values of $k$ does this equation have real solutions?

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