Practice Test 25 - Algebra 1

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

Let $g(x)=\dfrac{1}{x-5}$ . To keep $g$ a function with one output for each input, $g(x)$ must be defined for the input. For what values of $x$ is $g(x)$ defined? (Answer in words or interval notation.)
Add: $(2x^2 + 5x - 3) + (x^2 - 7x + 4)$
Subtract: $\left(6y^2 - 4y + 9\right) - \left(2y^2 + 7y - 1\right)$
Which expression is equivalent to $(x^2 + 2x - 8) + (3x^2 - 5x + 1)$ ?
A student wants a descriptive model of their phone use for the past 7 days. Which variable definitions are most appropriate and specific?
If $f(x) = x^2 + 2x$ and $g(x) = x - 3$ , which expression represents $(f \circ g)(x + 1)$ ?
Graph the step function $f(x)=\lfloor x\rfloor$ on the interval $-2\le x\le 3$ . Which statement is true about the graph?
Rewrite $27^{2/3}$ using radical notation and evaluate.
An investment is modeled by $A(t)=1500(1.02)^{12t}$ , where $t$ is in years. The base $1.02$ is applied each month. What is the monthly interest rate (as a percent)?
Which of the following correctly identifies the terms in $2p^3+3p-8$ ?
Multiply and simplify by factoring first (the result is a rational expression): $\frac{x^2+3x}{x^2-9}\cdot\frac{x-3}{x}$
A factory's total cost $C(w)$ (in dollars) depends on the number of widgets $w$ produced: $C(w)=50+8w$ . The number of widgets produced after $d$ days is $w(d)=12d$ . What does the composition $C(w(d))$ represent?
Explain the relationship between the equation $x^2+y^2=25$ and its graph.
Two functions are given: $p(x)=x^2+10x$ (quadratic) and $q(x)=1.5^x$ (exponential). Which statement about their long-term behavior is true?
The revenue function for a small business is $R(x) = -x^2 + 14x - 40$ , where $x$ is the number of items sold. What is the difference between the maximum revenue and the minimum value of the expression $x^2 - 14x + 40$ ?
Which set of statements is always true? I. rational + rational = rational II. irrational + irrational = irrational III. nonzero rational $\times$ irrational = irrational
In the expression $-7x + 2$ , what is the constant term?
Why must $16^{1/4}$ equal 2 if we want exponent properties to hold for rational exponents? Use the idea that $(b^{1/n})^n=b$ for $b>0$ .
A basketball coach wants a descriptive model summarizing the team's performance over the last 5 games. Which quantities are most relevant for describing performance?
A sequence is defined as a function on $n = 1, 2, 3, \dots$ by $a_1 = 9$ and $a_{n+1} = \dfrac{1}{3}a_n$ . What is $a_4$ ?

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