Practice Test 99 - Algebra 2

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

A coordinate-plane graph shows a function defined only on a limited interval. The curve starts at a filled point at $x=-2$ and ends at an open point at $x=4$ . (The curve exists for every $x$ between these values.) From the graph, what is the domain of the function?
A rideshare company estimates a driver's weekly earnings with $E = 18h + 60$ , where $E$ is earnings in dollars and $h$ is the number of hours worked in a week. In this function, interpret the parameter $18$ .
A quadratic function $y = ax^2 + bx + c$ has zeros at $x = m$ and $x = n$ , where $m < n$ . If the factored form is $y = 2(x + 3)(x - 5)$ , which statement about the zeros and their relationship is correct?
When dividing $a(x)=x^3-2x+5$ by the quadratic $b(x)=x^2+3x-1$ , what must be true about the remainder $r(x)$ in the division algorithm form $\dfrac{a(x)}{b(x)}=q(x)+\dfrac{r(x)}{b(x)}$ ?
Rewrite $\frac{x^3+4x^2-2x+7}{x+2}$ as $q(x)+\frac{r(x)}{x+2}$ , where $\deg(r)<\deg(x+2)$ .
Check if $f(x)=\dfrac{3x}{x+1}$ and $g(x)=\dfrac{x}{3-x}$ are inverses by verifying both $f(g(x))$ and $g(f(x))$ (where defined).
Write the system of equations as a single matrix equation $AX=B$ (use variable order $x, y$ ): $\begin{cases} 3x+2y=8\\ x-5y=-3 \end{cases}$
Apply the Rational Zeros Theorem to help factor completely: $P(x)=2x^3-5x^2-4x+3.$ First list possible rational zeros, then test to find the actual rational zero(s) and factor.
The polynomial $q(x) = x^4 - 5x^3 + 6x^2$ can be factored by first factoring out the greatest common factor. After complete factorization, which statement about the x-intercepts and their effect on the graph is correct?
Determine whether the function $f(x)=x^4-2x^2$ is even, odd, or neither.
Which restriction(s) make $f(x)=x^2-4x$ pass the horizontal line test and therefore have an inverse? (Choose the best answer.)
Use the geometric series formula $S_n=\dfrac{a(1-r^n)}{1-r}$ (for $r\ne 1$ ) to find the sum of the first 6 terms of the geometric series $3+6+12+24+48+96.$
On the complex plane, $z=a+bi$ corresponds to $(a,b)$ . The midpoint of the segment from $z_1$ to $z_2$ is $\dfrac{z_1+z_2}{2}$ . What is the midpoint of the segment joining $z_1=6$ and $z_2=2+4i$ ?
For $f(x)=\dfrac{(x-5)(x+1)}{x^2-25}$ , find the vertical asymptote(s) and any hole(s).
A company deposits money into an account at the end of each month. The first deposit is $200, and each month's deposit is $5\%$ larger than the previous month's deposit. What is the total amount deposited after $8$ months (ignore interest earned on the account itself)?
A quantity follows the model $Q(t)=Q_0\,(1.02)^{12t}$ , where $t$ is in years. Which equivalent form reveals the annual growth factor?
The polynomial identity $x^4 - y^4 = (x^2 + y^2)(x^2 - y^2)$ can be further factored. Which of the following represents the complete factorization of $81a^4 - 16b^4$ ?
A table gives values of $f(x)$ and $g(x)$ . Use it to identify the interval that contains a solution to $f(x)=g(x)$ . Table: - At $x=1.4$ : $f(x)=4.06$ , $g(x)=4.20$ - At $x=1.5$ : $f(x)=4.48$ , $g(x)=4.25$ - At $x=1.6$ : $f(x)=4.95$ , $g(x)=4.30$ Assume $f$ and $g$ are continuous on this interval. In which interval must a solution occur?
The function $f(x)=x^2-4x+3$ is not one-to-one on all real numbers, so it fails the horizontal line test. Which domain restriction makes $f$ invertible?
Use the polynomial division algorithm to write $\frac{2x^3+x^2-5x+3}{x-2}$ in the form $q(x)+\frac{r}{x-2}$ , where $\deg(r)<\deg(x-2)$ .

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