Practice Test 32 - Algebra 1

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

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1. Given $f(x)=\sqrt{x+4}$ and $g(x)=3x-1$, compute $(f\circ g)(5)$.
2. Given $p(x)=4(x-1)$, what does $p(5)$ equal?
3. What are the terms in $x^3+4x$?
4. Use the factored form $P(x)=-2(x-2)^2(x+1)$ to identify the zeros (with multiplicities), then sketch a rough graph showing where it crosses or touches the x-axis and the correct end behavior.
5. For the function $g(x)=x^4-2x^2$, does the function have symmetry? If so, what type?
6. Translate the recursive definition $a_1=7$ and $a_{n+1}=a_n-3$ into an explicit formula.
7. The graph shows function $r(x)$, which has x-intercepts at $x = -2$ and $x = 4$. Function $s(x) = (x + 1)(x - 3)$. Which statement correctly compares the x-intercepts of these functions?
8. Function $p$ is described as follows: "The function starts at a y-value of 5 when $x = 0$, decreases linearly to a minimum of -3 when $x = 4$, then increases linearly back to 5 when $x = 8$." Function $q(x) = |x - 3| + 1$. Which comparison of their ranges is correct?
9. For $m(x)=2x^2-x$, what does $m(-3)$ equal?​
10. A small print shop makes posters and flyers. Let $x$ be the number of posters and $y$ be the number of flyers. Constraints: - Each poster takes 3 minutes and each flyer takes 1 minute. - The shop has at most 120 minutes available: $3x+y\le 120$. - They must make at least 20 total items: $x+y\ge 20$. - They can make at most 50 flyers: $y\le 50$. - $x\ge 0$ and $y\ge 0$. Which constraints does the point $(x,y)=(30,40)$ violate?
11. Verify whether $(2,3)$ is a solution to the linear-quadratic system (i.e., satisfies BOTH equations). $\begin{cases} y = x^2 - 1 \\ y = 2x - 1 \end{cases}$
12. A polynomial is given by $P(x)=(x-3)^2(x+2)$. What are the x-intercepts, and how does the graph behave at each intercept (crosses or touches)?
13. A car rental company charges $35 per day plus $0.15 per mile driven. However, if a customer drives more than 200 miles in a day, they pay a flat rate of $75 for that day regardless of mileage. Which function correctly represents the daily cost $C(m)$ for driving $m$ miles?
14. For the function $p(x)=x^2+2x-8$, evaluate $p(0)$.
15. How can the expression $2\pi r(r+h)$ be viewed to reveal its structure? (View $r+h$ as one chunk.)
16. What is the solution to $3x + 7 = 22$?
17. Function $h$ is defined by the equation $h(x) = \sqrt{x + 3}$. Which statement about the domain of $h$ is correct?
18. Rewrite $\frac{x^2+6}{x-1}$ in the form $q(x)+\frac{r(x)}{x-1}$ using polynomial division, where $\deg(r)<\deg(x-1)$.
19. What is the domain of the function $f(x)=\sqrt{5-x}$?​
20. For $f(x) = x^2 - x$, what does $f(-3)$ equal?

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