Practice Test 23 - Algebra 1

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

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1. Given $f(x) = -2x + 6$, what does $f(-1)$ equal?
2. If $f(x) = 10 - 3x$, what is the value of $f(4)$?
3. Subtract the rational expressions and simplify (the difference is a rational expression, showing closure under subtraction): $\frac{x}{x-2}-\frac{3}{x-2}$
4. Solve for $x$: $6x+4=2(3x+2)$
5. Maya simplifies $3\sqrt{5} + \frac{2}{3\sqrt{5}}$ by first rationalizing the denominator of the second term. After rationalization, what type of number is the sum, and why?
6. Based on the revenue pattern shown, what type of growth model best describes this company's performance, and what would be the projected revenue for Q5?
7. A bouncing ball rises to $80\%$ of its previous height after each bounce. If the first bounce reaches $10$ ft, what is the total of the bounce heights for the first $5$ bounces? Sum the geometric series $10+10(0.8)+10(0.8)^2+10(0.8)^3+10(0.8)^4$ (so $a=10$, $r=0.8$, $n=5$).
8. Let $f(x)=x^2-4x+1$ and $g(x)=3x-5$. Find $(f+g)(x)$.
9. What is the domain of $f(x)=\sqrt{x+5}$?
10. A school cafeteria wants a descriptive model of how much food is thrown away during lunch each day (not predicting future waste). Which set of variables is most appropriate to track and define?
11. When the polynomial $P(x) = ax^3 + bx^2 + cx + d$ is added to $Q(x) = 2x^3 - x^2 + 3x - 5$, the result is a polynomial of degree 2. What must be true about the coefficient $a$?
12. Use polynomial division to express $\frac{2x^3+3x^2-5x+1}{x-2}$ in the form $q(x)+\frac{r(x)}{x-2}$, where $\deg(r)<\deg(x-2)$.
13. The temperature $T$ (in °F) of a cooling soup $t$ minutes after being removed from heat follows $T(t) = 72 + 128(0.92)^t$. A food safety expert notes that the soup should not be consumed once it reaches room temperature. What does the parameter 72 represent, and how does it relate to the cooling process?
14. What is the domain of the function $f(x)=\sqrt{5-x}$?
15. For the quadratic function $y=-x^2+4x-3$, does the parabola open up or down?
16. Based on the graph shown, what is the solution to the system of linear equations?
17. On a coordinate plane, graph $y=x^2-9$. What are the $x$-intercepts (as points)?
18. Interpret the compound interest expression $P(1+r)^n$ as the product of $P$ and a factor not depending on $P$. Which description matches?
19. The sequence is defined recursively by $a_1 = 2$ and $a_{n+1} = a_n + 4$. What is the explicit formula for $a_n$?
20. Why doesn't irrational $+\,$ irrational always equal irrational? Choose the option that correctly addresses this with valid reasoning.

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