Q1. If f(x) = 4x − 3, what is f(5)?
Substitute x=5: f(5) = 4(5) − 3 = 20 − 3 = ?
Q2. If g(x) = x² − 2, what is g(−4)?
g(−4) = (−4)² − 2. Remember: (−4)² = 16, not −16.
Q3. Is the relation {(1,3), (2,5), (1,7)} a function? Type YES or NO.
Look at the inputs (first values). Does any input repeat with a different output?
Q4. What is the domain of f(x) = √(x − 7)? Answer as: x ≥ _ (type just the number)
x ≥
The inside of a square root must be ≥ 0. Set x − 7 ≥ 0 and solve.
Q5. Let f(x) = 3x and g(x) = x + 2. What is f(g(4))?
Work inside-out. First find g(4) = 4 + 2 = 6. Then find f(6) = 3(6) = ?
Q6. If h(x) = 2x + 5, find x when h(x) = 19.
Set 2x + 5 = 19. Solve for x.
Q7. Given f(x) = x² + 3, find f(2x). Simplify. (Type without spaces: e.g. 4x^2+3)
Replace x with (2x): f(2x) = (2x)² + 3 = 4x² + 3
Q8. Is the graph of a circle a function? Type YES or NO.
Apply the vertical line test. Does a vertical line ever cross the circle at more than one point?
Q1. What is 'a' in the equation 5x² − 3x + 1 = 0?
In ax² + bx + c = 0, a is the coefficient of x².
Q2. Solve by factoring: x² + 9x + 20 = 0. Enter the smaller root.
Find two numbers that multiply to 20 and add to 9. Try 4 and 5.
Q3. Evaluate the discriminant of x² + 6x + 9 = 0.
Δ = b² − 4ac. Here a=1, b=6, c=9. Calculate 36 − 4(1)(9).
Q4. How many real solutions does x² + x + 1 = 0 have?
Find Δ = b²−4ac = 1−4(1)(1) = 1−4 = −3. Is this positive, zero, or negative?
Q5. The parabola y = 3x² − 12x + 7 — what is the x-coordinate of the vertex?
x = −b/(2a) = −(−12)/(2·3) = 12/6 = ?
Q6. Does y = −x² + 4 open upward or downward? Type UP or DOWN.
Look at the sign of a (the coefficient of x²). If a < 0, the parabola opens downward.
Q7. Factor: x² − 36. Type in the form (x+a)(x-b) without spaces.
Difference of squares: x² − k² = (x+k)(x−k). What is k when k²=36?
Q8. Complete the square: what do you add to x² + 10x to make it a perfect square?
Take half of the coefficient of x: 10/2 = 5. Then square it: 5² = ?
Q1. Find the slope through (3, 7) and (7, 15).
m = (y₂−y₁)/(x₂−x₁) = (15−7)/(7−3) = ?
Q2. What is the slope of y = −5x + 3?
In y = mx + b, m is the slope. Read it directly from the equation.
Q3. Write the equation of the line: slope = 3, y-intercept = −2. (Format: y=3x-2)
Use y = mx + b. Substitute m=3 and b=−2.
Q4. What is the slope of a line perpendicular to y = 2x + 1? Enter as a fraction like -1/2.
Perpendicular slope = negative reciprocal. Slope is 2, so flip and negate: −1/2.
Q5. Solve the system by substitution. y = x + 3 and 2x + y = 12. What is x?
Substitute y=x+3 into 2x+y=12: 2x+(x+3)=12 → 3x+3=12 → 3x=9 → x=?
Q6. Solve by elimination: x + y = 8 and x − y = 2. What is x?
Add the two equations: 2x = 10 → x = ?
Q7. What is the y-intercept of the line 3x + 2y = 12? Enter just the number.
Set x=0: 3(0)+2y=12 → 2y=12 → y=?
Q8. Are the lines y = 4x + 1 and y = 4x − 7 parallel, perpendicular, or neither? Type PARALLEL, PERPENDICULAR, or NEITHER.
Both lines have slope 4. Lines with the same slope and different y-intercepts are...?