TSIA2 Algebra Fundamentals 5

Question 1

What is the range of the function f(x) = x² + 3 for all real x?

Accepted Answer

y ≥ 3

Answer

Since x² ≥ 0 for all real x, the minimum value of f(x) is 0 + 3 = 3.

Question 2

Solve for x: (x/3) + (x/6) = 5

Accepted Answer

x = 10

Answer

Multiply through by 6: 2x + x = 30, so 3x = 30 and x = 10.

Question 3

Which set of ordered pairs represents a function?

Accepted Answer

{(2,3),(3,3),(4,3)}

Answer

In {(2,3),(3,3),(4,3)}, each x-value appears only once, satisfying the definition of a function.

Question 4

Factor completely: 6x² - 12x

Accepted Answer

6x(x - 2)

Answer

The GCF is 6x, giving 6x(x - 2) as the fully factored form.

Question 5

A number is increased by 40% and the result is 98. What is the original number?

Accepted Answer

70

Answer

Let n be the original: 1.40n = 98, so n = 98 / 1.40 = 70.

(TSIA2) Texas Success Initiative Assessment 2.0 Practice Test