Sat Math Function Quiz Worksheet With Answer Key (Page 2 of 3) in pdf

Sat Math Function Quiz Worksheet With Answer Key Page 2

SAT Math Function Quiz

Answers

First, ﬁnd f (2) by plugging in 2 for x in the expression 2x

5. We get f (2) =

2·2 5 = 4 5 = 1. Similarly, f (5) = 2·5 5 = 5. Then, f (2)+f (5) = 1+5 = 4,

so answer D is correct.

22/3 or 7.33

First, ﬁnd h(a). Whatever is inside the parentheses of a function gets substituted

for x in the given expression for the function. So here, h(a) = 3a + 5. Since

h(a) = 27, we have 3a + 5 = 27, so that 3a = 22 and a = 22/3 (or a = 7.33).

This question is typical on the SAT and ACT; it is asking us to go “backwards”.

Suppose that y = h(x). Instead of giving us x and asking us for y, it is giving us

y and asking us for x. Also, don’t be fooled by the use of the diﬀerent letters (h

instead of f for the function, and a instead of x); the math is the same.

Since f (a) = 4a

3 and f (a) = 9, then 4a

3 = 9 so that 4a = 12 and a = 3.

Similarly, f (b) = 4b 3 = 5 so that 4b = 8 and b = 2. Finally, f (a + b) = f (3 + 2) =

f (5) = 4 · 5

3 = 17. Answer E is correct.

We substitute the 2a inside the function parentheses for x in the expression x

This gives f (2a) = (2a)

1 = 4a

1. Since f (2a) = 35, we have 4a

1 = 35,

so that 4a

= 36, or a

= 9. Solving for a gives a = ±3, and answer B is correct.

Note that since there can be only one answer, 3 is not given as an answer choice.

In this case, don’t forget to substitute everything inside the parentheses into x. A

common mistake here is to square the a but not the 2, resulting in the expression

1 = 35, which is incorrect.

Since f (4) = 2(4)+4 = 12, and f (6) = 2(6)+4 = 16, then f (4)+f (6) = 12+16 = 28.

To ﬁgure out which answer is correct, we have to evaluate each one until we get 28

as the value. Since f (12) = 2(12) + 4 = 28, answer C is correct.

pg. 2

Sat Math Function Quiz Worksheet With Answer Key Page 2