Practice Test 55 - Algebra 2

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

Function $f$ is given in the table: $\begin{array}{c|cccc} x & -1 & 0 & 1 & 2\\ \hline f(x) & -3 & 1 & 5 & 9 \end{array}$ Function $g$ is given algebraically by $g(x)=4x+1$ . Which statement correctly compares the rate of change (slope) of $f$ and $g$ ?
A school is ordering $n$ identical calculators for students. The total cost is $C(n)=12.50n$ . Should the graph of $C$ versus $n$ be shown as discrete points or as a continuous curve, and why?
If $\log_b(m) = p$ and $\log_b(n) = q$ , which expression represents $\log_b\left(\frac{m^2}{n^3}\right)$ ?
Subtract and write the result in standard form. Be careful to distribute the negative sign to every term; by closure, the difference is a polynomial: $\left(4x^4 - 2x^2 + 3x - 9\right) - \left(x^4 + 5x^3 - 2x + 6\right) .$
On the complex plane, let $z_1=1+7i$ and $z_2=5-1i$ . Using $|z_1-z_2|$ for distance and $\dfrac{z_1+z_2}{2}$ for midpoint (the same as the coordinate formulas for $(a,b)$ and $(c,d)$ ), which option correctly gives both the distance and the midpoint?
A population model is given by $N(t)=A\,b^{ct},$ where $A$ is the initial amount, $b>0$ is the base, $c$ is a constant, and $t$ is time. If you view $b^{ct}$ as a single entity, which interpretation is correct?
Two relationships are shown below. Relationship 1: x: 0, 1, 2, 3; y: 7, 9, 11, 13 Relationship 2: x: 0, 1, 2, 3; y: 2, 4, 8, 16 Which statement is correct about constant rate of change?
Use the logarithm properties $\log_b(xy)=\log_b(x)+\log_b(y)$ , $\log_b\left(\frac{x}{y}\right)=\log_b(x)-\log_b(y)$ , and $\log_b(x^p)=p\log_b(x)$ to expand the expression: $\log_5\left(\frac{x^3\sqrt{y}}{z^2}\right).$ Write your answer as a sum/difference of logarithms.
Add and write the result in standard form: $\,(-4x^3+2x^2+x-8)+(6x^3-5x+3)\,$ . (This demonstrates closure under addition.)
Consider the expression $G(x)=x^2(x+1)-4(x+1).$ If you view $(x+1)$ as a single entity, which statement correctly describes the structure revealed by that chunking?
Simplify the expression $\left(2^3\right)^t$ using the power-of-a-power property.
Use the logarithm properties $\log_b(xy)=\log_b(x)+\log_b(y),\quad \log_b\left(\frac{x}{y}\right)=\log_b(x)-\log_b(y),\quad \log_b(x^p)=p\log_b(x)$ to expand the expression $\log\left(\frac{(mn)^4}{p}\right)$ (common log base 10) into a sum/difference of logs with no exponents inside the logs.
For the logarithmic function $h(x)=\ln(x+2)$ , which statement correctly describes its intercepts and asymptote? (Use the parent $y=\ln(x)$ .)
A savings account has $1200 and earns $3.2\%$ interest compounded annually. Create a model for the balance after $t$ years and determine the balance after 12 years. Round to the nearest cent.
Two students complete the square for $2x^2 + 8x - 3 = 0$ . Student A gets $2(x + 2)^2 = 11$ and Student B gets $(x + 2)^2 = \frac{11}{2}$ . Which statement about their work is correct?
Use structure to factor the expression completely. Notice that $x^4-y^4$ can be seen as a difference of squares more than once. Which rewriting is correct?
Functions $f$ and $g$ are defined by $f(x) = \frac{2x + 3}{x - 1}$ and $g(x) = \frac{x + 3}{x - 2}$ . To verify whether these functions are inverses of each other, a student computes $f(g(x))$ and obtains $\frac{8x + 3}{3x - 7}$ . What can be concluded about the relationship between $f$ and $g$ ?
Given that $(x - 4)$ is a factor of $h(x) = x^3 - 6x^2 + kx + 8$ , which statement about $h(x + 4)$ is necessarily true?
Complex numbers represent points: $z=a+bi\leftrightarrow(a,b)$ . The distance between $z_1=a+bi$ and $z_2=c+di$ is $|z_1-z_2|=\sqrt{(a-c)^2+(b-d)^2}$ , and the midpoint is $\dfrac{z_1+z_2}{2}$ . For $z_1=7-2i$ and $z_2=1+4i$ , what are the distance and the midpoint?
In the expression $4x^2 + 3x$ , is the number $4$ a term, a factor, or a coefficient?

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