Exploring Power Functions

Evaluate: f(x) = x^3 at x = 2.

• 4

• 10

• 6

• 8

Graph the function f(x) = x^2 and describe its shape.

• The graph of f(x) = x^2 is a circle.

• The graph of f(x) = x^2 is a parabola that opens upwards.

• The graph of f(x) = x^2 opens downwards.

• The graph of f(x) = x^2 is a straight line.

Identify the degree of the power function f(x) = 5x^4.

• 2

• 4

• 3

• 5

Solve the equation 3x^2 = 12 for x.

• x = 2 or x = -2

• x = -3

• x = 0

• x = 3

Apply the transformation: f(x) = (x - 1)^2 + 3. What is the vertex?

• (1, 3)

• (1, 1)

• (2, 4)

• (0, 2)

Evaluate: f(x) = 2x^5 at x = -1.

• 2

• -1

• 0

• -2

Graph the function f(x) = x^3 - 4 and identify its intercepts.

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

• X-intercept: (1.5874, 0), Y-intercept: (0, -4)

• X-intercept: (-1.5874, 0), Y-intercept: (0, 4)

• X-intercept: (0, 0), Y-intercept: (1, -4)

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

• As x approaches ±∞, f(x) → -∞.

• As x approaches ±∞, f(x) → 0.

• As x approaches ±∞, f(x) → ∞.

• As x approaches ±∞, f(x) oscillates between -1 and 1.

Solve for x: 4x^3 = 64.

• 4

• 1

• 2

• 3

Apply the transformation: f(x) = 2(x + 2)^3. What is the effect on the graph?

• The graph shifts right by 2 units and compresses vertically by a factor of 2.

• The graph shifts left by 2 units and stretches vertically by a factor of 2.

• The graph shifts down by 2 units and reflects over the x-axis.

• The graph shifts up by 2 units and stretches horizontally by a factor of 2.