AST Algebra and Functions 1 — Questions and Answers

Question 1: If f(x) = 3x² - 2x + 5, what is f(4)?

37
41
45 (Correct answer)
53

Correct answer: 45

f(4) = 3(16) - 2(4) + 5 = 48 - 8 + 5 = 45.

To evaluate f(4), replace every x with 4: f(4) = 3(4²) - 2(4) + 5. Calculate the exponent first: 4² = 16. Then multiply: 3 × 16 = 48 and 2 × 4 = 8. Finally, combine: 48 - 8 + 5 = 45. Always follow the order of operations (PEMDAS) when evaluating functions.

Question 2: What are the solutions to x² - 7x + 12 = 0?

x = 3 and x = 4 (Correct answer)
x = -3 and x = -4
x = 2 and x = 6
x = 1 and x = 12

Correct answer: x = 3 and x = 4

Factor: (x - 3)(x - 4) = 0, so x = 3 or x = 4.

To factor x² - 7x + 12, find two numbers that multiply to +12 and sum to -7. Those numbers are -3 and -4: (-3) × (-4) = 12 and (-3) + (-4) = -7. So the factored form is (x - 3)(x - 4) = 0. Setting each factor to zero gives x = 3 or x = 4.

Question 3: If 4x - 7 = 2x + 11, what is the value of x?

7
8
9 (Correct answer)
10

Correct answer: 9

4x - 2x = 11 + 7 → 2x = 18 → x = 9.

Start by subtracting 2x from both sides: 4x - 2x - 7 = 11, which simplifies to 2x - 7 = 11. Add 7 to both sides: 2x = 18. Finally, divide by 2: x = 9. Always verify by substituting back: 4(9) - 7 = 29 and 2(9) + 11 = 29. ✓

Question 4: Which of the following represents the slope-intercept form of 6x - 2y = 10?

y = 3x - 5 (Correct answer)
y = 3x + 5
y = -3x - 5
y = 6x - 10

Correct answer: y = 3x - 5

Solve for y: -2y = -6x + 10 → y = 3x - 5.

To convert to slope-intercept form (y = mx + b), isolate y. Subtract 6x from both sides: -2y = -6x + 10. Divide every term by -2: y = 3x - 5. The slope is 3 and the y-intercept is -5.

Question 5: A function is defined as g(x) = 2x + 3. What is g(g(2))?

13
15
17 (Correct answer)
19

Correct answer: 17

g(2) = 2(2) + 3 = 7. Then g(7) = 2(7) + 3 = 17.

This is a composite function problem. First evaluate the inner function: g(2) = 2(2) + 3 = 4 + 3 = 7. Then use 7 as the input to the outer g: g(7) = 2(7) + 3 = 14 + 3 = 17. Composite function notation g(g(2)) means apply g twice.

Question 6: What is the value of x in the equation √(2x + 6) = 8?

25
27
29 (Correct answer)
31

Correct answer: 29

Square both sides: 2x + 6 = 64 → 2x = 58 → x = 29.

To solve a radical equation, square both sides: (√(2x + 6))² = 8² → 2x + 6 = 64. Subtract 6: 2x = 58. Divide by 2: x = 29. Always verify: √(2(29) + 6) = √64 = 8. ✓

AST Algebra and Functions 1

If f(x) = 3x² - 2x + 5, what is f(4)?

Select your answer