SAT CollegeBoard Practice Test (1-8) Function

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1. (Test $1 / Q 10 /$ No Calculator)

$$ g(x)=a x^{2}+24 $$ For the function $g$ defined above, $a$ is a constant and $g(4)=8$. What is the value of $g(-4)$ ? A) 8 B) 0 C) $-1$ D) $-8$

2. (Test $1 / \mathrm{Q} 17 /$ Calculator)

The complete graph of the function $f$ is shown in the $x y$-plane above. For what value of $x$ is the value of $f(x)$ at its minimum? A) $-5$ B) $-3$ C) $-2$ D) 3

3. (Test $1 / \mathrm{Q} 36 /$ Calculator)

$$ h(x)=\frac{1}{(x-5)^{2}+4(x-5)+4} $$ For what value of $x$ is the function $h$ above undefined?

4. (Test2/Q 14/No Calculator)

A radioactive substance decays at an annual rate of 13 percent. If the initial amount of the substance is 325 grams, which of the following functions $f$ models the remaining amount of the substance, in grams, $t$ years later? A) $f(t)=325(0.87)^{t}$ B) $f(t)=325(0.13)^{t}$ C) $f(t)=0.87(325)^{t}$ D) $f(t)=0.13(325)^{t}$

5. (Test2/Q $10 /$ Calculator)

A function $f$ satisfies $f(2)=3$ and $f(3)=5$. A function $g$ satisfies $g(3)=2$ and $g(5)=6$. What is the value of $f(g(3))$ ? A) 2 B) 3 C) 5 D) 6

6. (Test $2 / Q: 33 /$ Calculator )

In the $x y$-plane, the point $(3,6)$ lies on the graph of the function $f(x)=3 x^{2}-b x+12$. What is the value of $b$ ?

7. (Test $3 / Q 4 /$ Calculator $)$

$$\begin{array}{|c||c|c|c|c|} \hline n & 1 & 2 & 3 & 4 \\ \hline f(n) & -2 & 1 & 4 & 7 \\ \hline \end{array}$$ The table above shows some values of the linear function $f$. Which of the following defines $f$ ? A) $f(n)=n-3$ B) $f(n)=2 n-4$ C) $f(n)=3 n-5$ D) $f(n)=4 n-6$

8. (Test $3 / \mathrm{Q} 17 /$ Calculator)

$$ \begin{aligned} &S(P)=\frac{1}{2} P+40 \\ &D(P)=220-P \end{aligned} $$ The quantity of a product supplied and the quantity of the product demanded in an economic market are functions of the price of the product. The functions above are the estimated supply and demand functions for a certain product. The function $S(P)$ gives the quantity of the product supplied to the market when the price is $P$ dollars, and the function $D(P)$ gives the quantity of the product demanded by the market when the price is $P$ dollars. How will the quantity of the product supplied to the market change if the price of the product is increased by $\$ 10$ ? A) The quantity supplied will decrease by 5 units. B) The quantity supplied will increase by 5 units. C) The quantity supplied will increase by 10 units. D) The quantity supplied will increase by 50 units.

9. (Test $3 / Q 18 /$ Calculator)

$$ \begin{aligned} &S(P)=\frac{1}{2} P+40 \\ &D(P)=220-P \end{aligned} $$ The quantity of a product supplied and the quantity of the product demanded in an economic market are functions of the price of the product. The functions above are the estimated supply and demand functions for a certain product. The function $S(P)$ gives the quantity of the product supplied to the market when the price is $P$ dollars, and the function $D(P)$ gives the quantity of the product demanded by the market when the price is P dollars, At what price will the quantity of the product supplied to the market equal the quantity of the product demanded by the market? A) $\$ 90$ B) $\$ 120$ C) $\$ 133$ D) $\$ 155$

10. (Test4/Q 2/No Calculator)

$$f(x)=\frac{3}{2} x+b$$ In the function above, $b$ is a constant. If $f(6)=7$, what is the value of $f(-2)$ ? A) $-5$ B) $-2$ C) 1 D) 7

11. (Test/A/Q 4/No Calculator)

If $f(x)=-2 x+5$, what is $f(-3 x)$ equal to? A) $-6 x-5$ B) $6 x+5$ C) $6 x-5$ D) $6 x^{2}-15 x$

12. (Test $4 / \mathrm{Q} 12 /$ Calculator)

In the $x y$-plane, the graph of function $f$ has $x$-intercepts at $-3,-1$, and 1 . Which of the following could define $f$ ? A) $f(x)=(x-3)(x-1)(x+1)$ B) $f(x)=(x-3)(x-1)^{2}$ C) $f(x)=(x-1)(x+1)(x+3)$ D) $f(x)=(x+1)^{2}(x+3)$

13. (Test $4 / \mathrm{Q} 13 /$ Calculator)

The population of mosquitoes in a swamp is estimated over the course of twenty weeks, as shown in the table. $$\begin{array}{|c|r|} \hline \text{Time (weeks) }& \text{Population }\\ \hline 0 & 100 \\ \hline 5 & 1,000 \\ \hline 10 & 10,000 \\ \hline 15 & 100,000 \\ \hline 20 & 1,000,000 \\ \hline \end{array}$$ Which of the following best describes the relationship between time and the estimated population of mosquitoes during the twenty weeks? A) Increasing linear B) Decreasing linear C) Exponential growth D) Exponential decay

14. (Test4/Q $25 /$ Calculator)

$$ \begin{aligned} &f(x)=2 x^{3}+6 x^{2}+4 x \\ &g(x)=x^{2}+3 x+2 \end{aligned} $$ The polynomials $f(x)$ and $g(x)$ are defined above. Which of the following polynomials is divisible by $2 x+3$ ? A) $h(x)=f(x)+g(x)$ B) $p(x)=f(x)+3 g(x)$ C) $r(x)=2 f(x)+3 g(x)$ D) $s(x)=3 f(x)+2 g(x)$

15. (Test4/Q 28/Calculator)

$$f(x)=(x+6)(x-4)$$ Which of the following is an equivalent form of the function $f$ above in which the minimum value of $f$ appears as a constant or coefficient? A) $f(x)=x^{2}-24$ B) $f(x)=x^{2}+2 x-24$ C) $f(x)=(x-1)^{2}-21$ D) $f(x)=(x+1)^{2}-25$

16. (Test5/Q 4/No Calculator)

Which of the following is an example of a function whose graph in the $x y$-plane has no $x$-intercepts? A) A linear function whose rate of change is not zero B) A quadratic function with real zeros C) A quadratic function with no real zeros D) A cubic polynomial with at least one real zero

17. (Test $5 / Q 2 /$ Calculator)

$$\begin{array}{|c|c|} \hline x & f(x) \\ \hline 1 & 5 \\ \hline 3 & 13 \\ \hline 5 & 21 \\ \hline \end{array}$$ Some values of the linear function $f$ are shown in the table above. Which of the following defines $f$ ? A) $f(x)=2 x+3$ B) $f(x)=3 x+2$ C) $f(x)=4 x+1$ D) $f(x)=5 x$

18. (Test6/Q 8/No Calculator)

$$\begin{array}{|c|c|c|} \hline x & w(x) & \mathrm{t}(x) \\ \hline 1 & -1 & -3 \\ \hline 2 & 3 & -1 \\ \hline 3 & 4 & 1 \\ \hline 4 & 3 & 3 \\ \hline 5 & -1 & 5 \\ \hline \end{array}$$ The table above shows some values of the functions $w$ and $t$. For which value of $x$ is $w(x)+t(x)=x$ ? A) 1 B) 2 C) 3 D) 4

19. (Test6/Q 25/Calculator)

$$\begin{array}{|r|r|} \hline x & f(x) \\ \hline 0 & -2 \\ \hline 2 & 4 \\ \hline 6 & 16 \\ \hline \end{array}$$ Some values of the linear function $f$ are shown in the table above. What is the value of $f(3)$ ? A) 6 B) 7 C) 8 D) 9

20. (Test $7 / Q 5 /$ No Calculator)

If $f(x)=\frac{x^{2}-6 x+3}{x-1}$, what is $f(-1)$ ? A) $-5$ B) $-2$ C) 2 D) 5

21. (Test8/Q 15/No Calculator)

$$ \begin{aligned} &g(x)=2 x-1 \\ &h(x)=1-g(x) \end{aligned} $$ The functions $g$ and $h$ are defined above. What is the value of $h(0)$ ? A) $-2$ B) 0 C) 1 D) 2

22. (Test $8 / \mathrm{Q} ; 35 /$ Calculator)

The graph of the function $f$, defined by $f(x)=-\frac{1}{2}(x-4)^{2}+10$, is shown in the $x y$-plane above. If the function $g$ (not shown) is defined by $g(x)=-x+10$, what is one possible value of $a$ such that $f(a)=g(a)$ ?

23. (Test6/Q 15/Calculator)

$$\begin{array}{|c|c|c|c|c|c|} \hline x & 1 & 2 & 3 & 4 & 5 \\ \hline y & \frac{11}{4} & \frac{25}{4} & \frac{39}{4} & \frac{53}{4} & \frac{67}{4} \\ \hline \end{array}$$ Which of the following equations relates $y$ to $x$ for the values in the table above? A) $y=\frac{1}{2} \cdot\left(\frac{5}{2}\right)^{x}$ B) $y=2 \cdot\left(\frac{3}{4}\right)^{x}$ C) $y=\frac{3}{4} x+2$ D) $y=\frac{7}{2} x-\frac{3}{4}$

24. (Test7/Q 25/Calculator)

Energy per Gram of Typical Macronutrients $$\begin{array}{|l|c|c|} \hline \text{Macronutrient} & \text{Food calories} &\text{ Kilojoules }\\ \hline \text{Protein} & 4.0 & 16.7 \\ \hline \text{Fat} & 9.0 & 37.7 \\ \hline \text{Carbohydrate }& 4.0 & 16.7 \\ \hline \end{array}$$ The table above gives the typical amounts of energy per gram, expressed in both food calories and kilojoules, of the three macronutrients in food. If $x$ food calories is equivalent to $k$ kilojoules, of the following, which best represents the relationship between $x$ and $k$ ? A) $k=0.24 x$ B) $k=4.2 x$ C) $x=4.2 k$ D) $x k=4.2$

25. (Test $7 / \mathrm{Q} 26 /$ Calculator)

Energy per Gram of Typical Macronutrients $$\begin{array}{|l|c|c|} \hline \text{Macronutrient} & \text{Food calories} & \text{Kilojoules }\\ \hline \text{Protein} & 4.0 & 16.7 \\ \hline \text{Fat} & 9.0 & 37.7 \\ \hline \text{Carbohydrate }& 4.0 & 16.7 \\ \hline \end{array}$$ The table above gives the typical amounts of energy per gram, expressed in both food calories and kilojoules, of the three macronutrients in food. If the 180 food calories in a granola bar come entirely from $p$ grams of protein, $f$ grams of fat, and $c$ grams of carbohydrate, which of the following expresses $f$ in terms of $p$ and $c$ ? A) $f=20+\frac{4}{9}(p+c)$ B) $f=20-\frac{4}{9}(p+c)$ C) $f=20-\frac{4}{9}(p-c)$ D) $f=20+\frac{9}{4}(p+c)$

26. (Test8/Q 2/No Calculator)

The graph above shows the distance traveled $d$, in feet, by a product on a conveyor belt $m$ minutes after the product is placed on the belt. Which of the following equations correctly relates $d$ and $m$ ? A) $d=2 m$ B) $d=\frac{1}{2} m$ C) $d=m+2$ D) $d=2 m+2$

27. (Test8/Q 5/No Calculator)

The width of a rectangular dance floor is $w$ feet. The length of the floor is 6 feet longer than its width. Which of the following expresses the perimeter, in feet, of the dance floor in terms of w ? A) $2 w+6$ B) $4 w+12$ C) $w^{2}+6$ D) $w^{2}+6 w$

Answer

1 A	$\quad$ Explanation
2 B	$\quad$ Explanation
3 3	$\quad$ Explanation
4 A	$\quad$ Explanation
5 B	$\quad$ Explanation
6 11	$\quad$ Explanation
7 C	$\quad$ Explanation
8 B	$\quad$ Explanation
9 B	$\quad$ Explanation
10 A	$\quad$ Explanation
11 B	$\quad$ Explanation
12 C	$\quad$ Explanation
13 C	$\quad$ Explanation
14 B	$\quad$ Explanation
15 D	$\quad$ Explanation
16 C	$\quad$ Explanation
17 C	$\quad$ Explanation
18 B	$\quad$ Explanation
19 B	$\quad$ Explanation
20 A	$\quad$ Explanation
21 D	$\quad$ Explanation
22 2,8	$\quad$ Explanation
23 D	$\quad$ Explanation
24 B	$\quad$ Explanation
25 B	$\quad$ Explanation
26 A	$\quad$ Explanation
27 B	$\quad$ Explanation