Exploring Power Function Graphs

What is the general form of a power function?

• f(x) = k - x^n

• f(x) = k * x^n

• f(x) = k + x^n

• f(x) = k / x^n

Identify the graph of the function f(x) = x^3.

• The graph of f(x) = x^3 is a straight line that slopes upwards.

• The graph of f(x) = x^3 is a circular curve centered at the origin.

• The graph of f(x) = x^3 is a parabolic curve that opens downwards.

• The graph of f(x) = x^3 is a cubic curve that passes through the origin and has a characteristic S-shape.

Analyze the end behavior of the function f(x) = -2x^4.

• As x approaches ±∞, f(x) → -∞.

• As x approaches 0, f(x) → 0.

• As x approaches ±∞, f(x) → 2.

• As x approaches ±∞, f(x) → ∞.

Determine the x-intercept of the function f(x) = x^2 - 4.

• x = 0

• x = 2 and x = -2

• x = 1

• x = -1

What transformation occurs when the function f(x) = x^2 is changed to f(x) = (x-3)^2?

• The graph shifts 3 units to the left.

• The graph reflects over the x-axis.

• The graph shifts 3 units up.

• The graph shifts 3 units to the right.

Compare the graphs of f(x) = x^2 and g(x) = x^4.

• The graph of g(x) = x^4 is steeper than the graph of f(x) = x^2 for |x| > 1.

• Both graphs intersect at all points on the x-axis.

• The graph of g(x) = x^4 is a straight line.

• The graph of f(x) = x^2 is always above the graph of g(x) = x^4.

What is the y-intercept of the function f(x) = 3x^5?

• 3

• 0

• -3

• 1

Identify the graph that represents f(x) = -x^3 + 1.

• The graph of f(x) = -x^3 + 1 is a downward-opening cubic curve with a maximum point at (0, 1).

• The graph of f(x) = -x^3 + 1 is a downward-opening parabola with a vertex at (0, 1).

• The graph of f(x) = -x^3 + 1 is an upward-opening cubic curve with a minimum point at (0, 1).

• The graph of f(x) = -x^3 + 1 is a straight line with a slope of -1.

Analyze the end behavior of f(x) = x^5.

• rises to the left and falls to the right.

• The end behavior is: rises to the right and falls to the left.

• remains constant as x approaches infinity.

• falls to both the left and the right.

Determine the intercepts of the function f(x) = x^2 + 2x + 1.

• X-intercept: (-2, 0), Y-intercept: (0, 2)

• X-intercept: (0, 1), Y-intercept: (-1, 0)

• X-intercept: (1, 0), Y-intercept: (0, -1)

• X-intercept: (-1, 0), Y-intercept: (0, 1)