#1
Which of the following is a linear function?
y = 2x + 3
ExplanationLinear functions have a constant rate of change.
#2
Solve for x: 2x + 5 = 13
x = 6
ExplanationIsolate x by subtracting 5 from both sides, then divide by 2.
#3
If f(x) = 3x - 2, find f(4).
10
ExplanationReplace x with 4 in the function and evaluate.
#4
What is the domain of the function g(x) = sqrt(2x - 5)?
x > 5/2
ExplanationThe expression under the square root cannot be negative.
#5
Simplify the expression: (2x^2 - 5x + 3) / (x - 1)
2x + 3
ExplanationUse polynomial long division or factorization.
#6
If k(x) = |2x - 7|, what is the range of k?
k ≥ 0
ExplanationAbsolute value functions output non-negative values.
#7
Solve the inequality: 2x - 7 > 3x + 1
x < -8
ExplanationIsolate x by subtracting 2x from both sides.
#8
Find the sum of the roots of the quadratic equation: x² - 6x + 9 = 0.
3
ExplanationSum of roots for a quadratic ax² + bx + c = 0 is -b/a.
#9
If q(x) = 4x² - 16, what is the vertex of the parabola represented by q?
(4, 0)
ExplanationThe vertex of the parabola is at (-b/2a, q(-b/2a)).
#10
If h(x) = (x + 1)/(x - 3), find the vertical asymptote.
x = 3
ExplanationVertical asymptotes occur where the denominator equals zero.
#11
Evaluate the expression: log₂(16) + log₂(8)
6
ExplanationCombine logarithms using the property log(a) + log(b) = log(ab).
#12
If p(x) = x³ - 4x² + 5x - 2, find the critical points of p.
x = 1, x = 3
ExplanationCritical points occur where the derivative equals zero.
#13
Find the inverse function of f(x) = 2x + 4.
f⁻¹(x) = (x - 4)/2
ExplanationSwap x and y, then solve for y.
#14
If m(x) = e^(3x), what is the derivative of m with respect to x?
3e^(3x)
ExplanationUse the chain rule: d(e^u)/dx = u'(x)e^u.
#15
Evaluate the limit as x approaches 2 for the function: f(x) = (x² - 4) / (x - 2)
6
ExplanationTry direct substitution or factorization.
#16
If n(x) = 2^(4x), what is the logarithmic form of n?
log₂(2^4)
ExplanationConvert exponentiation to logarithmic form.