Bluebook SAT Test Algebra and Functions 3

Question 1

If h(x) = x² - 2x + 5, what is h(x + 1)?

Accepted Answer

x² + 4

Answer

(x+1)² - 2(x+1) + 5 = x²+2x+1-2x-2+5 = x²+4.

Question 2

For what value of x does the function f(x) = (x - 2)/(x² - 9) have a vertical asymptote?

Accepted Answer

x = 3 and x = -3

Answer

Vertical asymptotes occur where denominator = 0: x²-9 = 0 → x = ±3. x=2 is not a zero of the denominator.

Question 3

If f(x) = 3x - 1 and g(f(x)) = x, what is g(x)?

Accepted Answer

(x + 1)/3

Answer

g is the inverse of f. Solving y = 3x-1 for x: x = (y+1)/3. So g(x) = (x+1)/3.

Question 4

A function f is increasing for all x. Which of the following could be f?

Accepted Answer

f(x) = 2^x

Answer

f(x) = 2^x is always increasing (exponential growth). The others decrease on parts of their domains.

Question 5

The function p(x) = ax + b satisfies p(2) = 7 and p(5) = 13. What is a + b?

Accepted Answer

5

Answer

Slope a = (13-7)/(5-2) = 2. p(2) = 2(2)+b = 7 → b = 3. a+b = 2+3 = 5.

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