Practice Test 33 - Algebra 2

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

Construct a linear function $p(x)$ with slope $m=-3$ that passes through the point $(2,11)$ . Which formula is correct?
Describe the graph's behavior based on factored form: $h(x)=(x+1)^4(x-3).$ Identify the zeros with multiplicities, state whether the graph crosses or touches at each zero, and determine the end behavior.
Is $(x+2)$ a factor of $p(x)=x^3+3x^2-4x-12$ ? Use the Remainder Theorem / Factor Theorem (i.e., $(x-a)$ is a factor iff $p(a)=0$ ).
Use logarithms to solve $7\cdot 2^{5t}=120$ for $t$ . Express the solution as a logarithm (base 2) and evaluate using a calculator.
Solve the quadratic equation. (Choose any method.) $x^2+3x-1=0.$
Add the polynomials (combine like terms). This illustrates the closure property because the sum of two polynomials is also a polynomial: $(2x^4-3x^3+x^2-5)+(x^4+2x^3-4x^2+x+3).$
Use the inverse relationship between exponents and logarithms to evaluate $\log_2(32)$ . (Recall: $b^y=x \Leftrightarrow \log_b(x)=y$ .)
Use conjugates to rationalize the denominator and write in standard form $a+bi$ : $\frac{2-i}{3+2i}.$
Solve for $x$ and evaluate using technology: $8\cdot 2^{x/2}=70$ . Express the exact solution as a logarithm.
Use the Remainder Theorem to find the remainder when $p(x)=3x^3-x^2-7x+2$ is divided by $(x+2)$ .
Use the Rational Zeros Theorem to list all possible rational zeros of $P(x)=4x^3-3x^2-8x+6.$ (List each candidate in lowest terms; include both signs.)
Find the oblique (slant) asymptote of $f(x)=\frac{x^2+3x+2}{x+1}.$
Which situation represents a constant rate of change (linear relationship)?
The geometric sequence is $5, 15, 45, 135, \dots$ where the term number is $x$ (so $x=1$ gives 5). Write an exponential function $g(x)$ that gives the $x$ th term.
On the complex plane, $z=a+bi$ corresponds to the point $(a,b)$ . For $z_1=-1+4i$ and $z_2=3$ , which complex number is the midpoint of the segment connecting them, using $\dfrac{z_1+z_2}{2}$ ?
A company's revenue is modeled by $R(t)=75,000(1.10)^t$ , where $t$ is the number of years since the company launched. What is the annual growth rate of the revenue in this model?
For $f(x)=\frac{(x-5)(x+2)}{(x-5)(x-1)}$ identify the zero(s), vertical asymptote(s), any hole (removable discontinuity), and the horizontal asymptote.
One printer can print a batch of flyers in 10 minutes. A second printer can print the same batch in 15 minutes. If both printers run together, how long will it take to print one batch? Write and solve an equation to find the time. Let $t$ = time in minutes to print one batch together.
Function $r$ is given by the equation $r(x) = 2^{x-1} + 3$ . The table represents function $s$ . Which statement about the horizontal asymptotes of these functions is correct?
A cell phone plan charges a monthly base fee plus a fixed rate per text message. In January, Sarah sent 120 text messages and paid $32. In February, she sent 180 text messages and paid $38. Which expression represents the total monthly cost $C$ as a function of the number of text messages $t$ ?

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