Practice Test 17 - Algebra 2

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

An investment follows the model $A(t)=1200(1.06)^t$ , where $t$ is in years. What is the constant percent rate, and does the model represent exponential growth or decay?
Function $f$ is given by $f(x)=2^x$ . Function $g$ is represented numerically by the table. \begin{center} \begin{tabular}{c|c} $x$ & $g(x)$ \\\hline $0$ & $3$ \\ $1$ & $6$ \\ $2$ & $12$ \\ $3$ & $24$ \\ \end{tabular} \end{center} Which statement correctly compares the growth factor (multiplier per increase of 1 in $x$ ) of $f$ and $g$ ?
A function is described as follows: It starts at the point $(0,2)$ , increases to a relative maximum at $(3,5)$ , then decreases crossing the x-axis at $x=6$ , and continues decreasing as $x$ increases. As $x\to -\infty$ , the function decreases without bound. Sketch a graph showing all of these features.
Graph the exponential function $f(x)=3\cdot 2^x$ showing the y-intercept, horizontal asymptote, and end behavior.
For the logarithmic function $g(x)=\log_2(x-3)$ , what is the vertical asymptote? (Relate to the parent $y=\log_2(x)$ and horizontal shifts.)
The distance between $z_1=a+bi$ and $z_2=c+di$ is the modulus $|z_1-z_2|=\sqrt{(a-c)^2+(b-d)^2}$ . What is the distance between $z_1=0$ and $z_2=6+8i$ ?
How many real solutions (intersection points) does the system have? $\begin{cases} y = x^2 + 4 \\ y = 2x + 1 \end{cases}$
A bike rental shop charges a fixed fee of $12 plus $4 per hour. Write an equation for the total cost $C$ (dollars) in terms of the number of hours $h$ , and choose appropriate axes labels and a reasonable scale to graph the relationship for $0 \le h \le 8$ .
Solve for $t$ : $12\cdot 2^{t/4}=100$ . Give the exact solution as a logarithm and then approximate using technology.
The polynomial $f(x) = 2x^3 - 8x^2 + 6x$ can be factored completely. Which statement best describes the behavior of the graph of $y = f(x)$ near its zeros?
Graph $p(x)=-(x+2)(x-1)^2(x-4)$ showing zeros, whether the graph crosses or touches at each zero, and the correct end behavior.
Solve the system by elimination. Give the solution as an ordered pair $(x,y)$ . $\begin{cases} x + y = 7 \\ 2x - y = 8 \end{cases}$
A sequence can be viewed as a discrete function whose domain is the positive integers. For the Fibonacci sequence defined by $f(1)=f(2)=1$ and $f(n)=f(n-1)+f(n-2)$ for $n\ge 3$ , find $f(7)$ .
Simplify the complex fraction. Because rational expressions are closed under $\div$ (by nonzero), the result is still a rational expression in lowest terms. $\displaystyle \frac{\frac{x}{x-2}}{\frac{3}{x+1}}$
Which statement about $\log_4\left(\frac{x^3y^2}{z^{1/2}}\right)$ is correct when $x, y, z > 0$ ?
A profit model is $P(x)=x^2-8x+15$ , where $x$ is the number of items sold (in tens). Factor $P(x)$ to find the break-even points (zeros), and state the corresponding x-intercepts.
Factor $P(x)=x^2+2x+5$ over the complex numbers. (This quadratic has no real zeros, but it does factor over $\mathbb{C}$ .) Which factorization is correct?
Expand the expression using logarithm properties: $\log\left(\frac{10x\sqrt{y}}{z^2}\right)$ (Here $\log$ is base 10.)
A company charges a one-time setup fee of $75 plus $18 per shirt. Create an inequality for a budget of at most $500 and find the maximum number of shirts that can be ordered. Let $n$ = the number of shirts (a whole number).
A rectangle has length $(x+5)$ and width $(x-2)$ , where $x$ is in inches. Write an equation for the area $A$ (square inches) in terms of $x$ , and choose appropriate axes labels and a reasonable scale to graph $A$ for $0\le x\le 10$ .

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