Practice Test 2 - Algebra 1

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

What value of $x$ makes the equation true? $\frac{x}{3}+2=7$
For the function $r(x) = |x - 4| + 3$ , which of the following correctly represents the meaning of the equation $r(a) = r(10)$ where $a ≠ 10$ ?
Solve $x^2-2x+10=0$ . Express both solutions in $a+bi$ form, using $\sqrt{-1}=i$ (so $i^2=-1$ ).
Compare the growth rates of $f(x)=4x$ (linear), $g(x)=x^3$ (polynomial), and $h(x)=3^x$ (exponential) for $x>10$ . Which statement is true for sufficiently large $x$ ?
The table shows values for a quadratic function $f(x)$ . Based on this data, what is the approximate $x$ -coordinate where $f(x)$ changes from decreasing to increasing?
An investment formula is given by $A = P(1 + r)^t + 500(1 + r)^{t-2}$ . To better understand the structure of this expression, which decomposition most clearly reveals the relationship between the terms?
A store sign lists a product weight as 1.50 lb. The scale used in the store reads to the nearest 0.1 lb. Identify the false precision in the statement.
Given $f(x) = x^2 - 4x - 12$ , a student factors this as $(x - 6)(x + 2)$ and identifies key features. Which analysis of the parabola's symmetry is correct?
Solve the system: $\begin{cases} 3x-y=7 \\ x+y=5 \end{cases}$ What is the solution $ (x, y) $?
Where is the vertex of $g(x)=|x-3|+2$ ?
A community garden is planting tomatoes and peppers. Let $x$ = number of tomato plants and $y$ = number of pepper plants. Constraints: - There is space for at most 30 plants total: $x+y\le 30$ . - Tomato plants must be at least 10: $x\ge 10$ . - Each tomato plant needs 2 minutes/day of watering and each pepper plant needs 3 minutes/day; they have at most 75 minutes/day: $2x+3y\le 75$ . - $x$ and $y$ must be nonnegative whole numbers. Is the point $(12, 6)$ a viable solution? Explain by identifying whether it satisfies all constraints.
A parabola is defined by $h(x)=-(x-4)^2+1$ . What is the maximum value of $h(x)$ ?
The function $p(x)=\sqrt{x}$ assigns one output to each input in its domain. What is the range of $p$ ? (Answer in interval notation.)
If $\sqrt[3]{x^2} = x^{\frac{a}{b}}$ where $\frac{a}{b}$ is in lowest terms, what is the value of $a + b$ ?
For the linear function $p(x)=4x-7$ , what is the average rate of change of $p(x)$ from $x=-2$ to $x=3$ ?
Divide and simplify (write your answer as a simplified rational expression): $\frac{x^2-4}{x+1}\div\frac{x+2}{x+1}$
A quadratic equation of the form $x^2 + bx + c = 0$ has solutions $x = 3 \pm 2i$ . What is the value of $b + c$ ?
The profit $P$ (in dollars) from selling $x$ items is given by $P(x) = -3x^2 + 24x - 36$ . How many items should be sold to maximize profit, and what is the maximum profit?
If $g(x)=x^2+3x-4$ , what is $g(-2)$ ?
Let $f(x)=2x$ and $g(x)=x^2+1$ . What is $f(g(3))$ ?

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