Practice Test 29 - Algebra 1

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

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1. Let $f(x)=\sqrt{x}$ and $g(x)=\dfrac{1}{x}$. Find the domain of $(f+g)(x)$.
2. A carpenter has 48 feet of trim and 20 square feet of plywood. Small shelves use 3 feet of trim and 2 square feet of plywood. Large shelves use 6 feet of trim and 4 square feet of plywood. If the carpenter makes $s$ small shelves and $\ell$ large shelves, which constraint is NOT properly represented?
3. Order the following functions by growth rate for large $x$ (from slowest-growing to fastest-growing): $f(x)=7x$ (linear), $g(x)=x^4$ (polynomial), $h(x)=1.1^x$ (exponential), $k(x)=3x^2$ (quadratic).
4. A taxi charges a base fee of $3.50 plus $2.00 per mile. The distance is measured in miles. Which expression has correct units for the total cost $C$ (in dollars) for $d$ miles?
5. A savings account grows by 8% per year, modeled by $(1.08)^t$ for $t$ years. What is the approximate monthly growth factor (so that $(1.08)^t \approx (\text{monthly factor})^{12t}$)?
6. Simplify using exponent properties: $(x^{2/3})^{3/2}$.​
7. A bakery makes muffins and cookies. Let $x$ be the number of muffin batches and $y$ be the number of cookie batches. Constraints: - Each muffin batch takes 2 hours and each cookie batch takes 3 hours. - The bakery has at most 18 hours available. - Each muffin batch uses 4 cups of flour and each cookie batch uses 2 cups of flour. - The bakery has at most 24 cups of flour. - $x\ge 0$ and $y\ge 0$. Which constraints does the point $(x,y)=(6,2)$ violate?
8. Is the point $(2,3)$ on the graph of $y=x^2-1$? Use substitution to decide. Substitute: $3=2^2-1$.
9. Use the geometric series sum formula $S_n=\frac{a(1-r^n)}{1-r}$ (for $r\ne 1$) to find the sum of the first 6 terms of the geometric series $5+10+20+40+\cdots$. (Here $a=5$, $r=2$, $n=6$.)
10. In the function $g(x)=\left(\frac{x-3}{2}\right)^2,$ what is being squared? (View the entire fraction as a single unit.)
11. For the linear function $y=-x-2$, at what point does the graph cross the $y$-axis?
12. The graph of a linear function is shown. Which equation best represents this function?
13. In the expression $-x+9$, what is the coefficient of $x$?
14. A rectangular garden has length 12 ft and width 9 ft. Using $A=\ell\times w$, what is the area, and what units should the answer have?
15. A school club is buying snacks for an event. Let $x$ be the number of boxes of granola bars and $y$ be the number of boxes of fruit snacks. Each granola bar box costs $6 and each fruit snack box costs $4. The club has at most $60 to spend and needs at least 12 total boxes. Also, $x$ and $y$ cannot be negative. Which system of inequalities models these constraints?
16. Use polynomial division to rewrite $\frac{x^3-x^2-4x+4}{x-2}$ as $q(x)+\frac{r(x)}{x-2}$, with $\deg(r)<\deg(x-2)$.
17. For the quadratic function $y=2x^2-8x+6$, what is the $y$-intercept (as a point) to label on the graph?
18. A town's population starts at 1000 people and increases by 10% each year. Which exponential function models the population after $t$ years?
19. Two lengths are measured as 3.2 m and 8.75 m. You multiply them to find an area: $3.2\times 8.75=28.0$ (from the calculator). How should the product be reported given the measurement precision?
20. In the expression $3(x+2)$, what are the factors?

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