MDTP Algebra 3

Question 1

Which equation represents a function with a slope of -2 and y-intercept of 4?

Accepted Answer

y = -2x + 4

Answer

Using y = mx + b with m = -2 and b = 4 gives y = -2x + 4.

Question 2

Simplify: (x³)⁴

Accepted Answer

x¹²

Answer

When raising a power to a power, multiply the exponents: 3 × 4 = 12, giving x¹².

Question 3

What is the solution set of x² - 5x + 6 = 0?

Accepted Answer

{2, 3}

Answer

Factoring gives (x - 2)(x - 3) = 0, so x = 2 or x = 3.

Question 4

If g(x) = x - 3 and h(x) = 2x, what is h(g(5))?

Accepted Answer

4

Answer

g(5) = 5 - 3 = 2, then h(2) = 2(2) = 4.

Question 5

What is the range of f(x) = x² + 1?

Accepted Answer

y ≥ 1

Answer

Since x² ≥ 0 for all x, x² + 1 ≥ 1, so the range is y ≥ 1.

MDTP - Mathematics Diagnostic Testing Project Practice Test