#1
What is the domain of the function f(x) = √(x + 3)?
(-3, ∞)
ExplanationSquare root function, valid for all real numbers greater than -3.
#2
What is the range of the function g(x) = 2x^2 - 5x + 3?
(-∞, 0]
ExplanationQuadratic function, outputs all real numbers less than or equal to 0.
#3
What is the inverse of the function h(x) = 4x - 7?
h^(-1)(x) = (x - 7) / 4
ExplanationFinding inverse by swapping x and y and solving for y.
#4
Which of the following functions is odd?
f(x) = x^3 - x
ExplanationOdd function: f(-x) = -f(x), with odd powers.
#5
Which of the following functions is even?
f(x) = x^4 - 2x^2
ExplanationEven function: f(-x) = f(x), even powers.
#6
What is the average rate of change of the function f(x) = 2x^2 - 3x over the interval [1, 3]?
1
ExplanationAverage rate of change = (f(3) - f(1)) / (3 - 1).
#7
What is the maximum or minimum value of the function f(x) = x^2 - 4x + 3?
Minimum value: 1
ExplanationFinding vertex of the quadratic function.
#8
Which of the following functions is neither even nor odd?
f(x) = 3x^2 + 2x
ExplanationFunction with mixed even and odd powers.
#9
What are the x-intercepts of the function y = (x - 2)(x + 3)?
{2, -3}
Explanationx-intercepts where y equals 0, roots of the equation.
#10
Which of the following statements about even functions is true?
Even functions are symmetric about the y-axis.
ExplanationEven functions have symmetry about the y-axis.
#11
What is the range of the function f(x) = 1/x?
(-∞, 0) ∪ (0, ∞)
ExplanationRange of rational function with no discontinuities.
#12
What is the value of f(g(2)) if f(x) = x^2 and g(x) = 2x - 1?
25
ExplanationComposing functions, g(2) = 3, then f(3) = 9.
#13
For the function f(x) = |x|, what is f(-3)?
1
ExplanationAbsolute value function gives positive output.
#14
What are the critical points of the function f(x) = x^3 - 6x^2 + 9x?
{0, 3}
ExplanationPoints where derivative equals zero or is undefined.