Exploring Power Functions

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

• 8

• 4

• 10

• 6

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

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

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

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

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

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

• odd function

• maximum at (0,0)

• Characteristics of f(x) = x^4: even function, degree 4, minimum at (0,0), continuous, differentiable, approaches infinity as |x| increases.

• degree 3

Solve the equation x^3 = 27.

• 3

• 4

• 2

• 5

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

• f(x) = (x + 1)^2 + 3 shifts the graph left by 1 unit.

• f(x) = (x - 1)^2 - 3 shifts the graph down by 3 units.

• f(x) = (x + 1)^2 - 3 shifts the graph left by 1 unit and down by 3 units.

• f(x) = (x - 1)^2 + 3 is a transformation that shifts the graph of y = x^2 to the right by 1 unit and up by 3 units.

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

• 2

• 0

• -2

• -1

Graph the function f(x) = x^(-2) and discuss its asymptotes.

• The function f(x) = x^(-2) has a vertical asymptote at x = 1.

• The function f(x) = x^(-2) has a vertical asymptote at x = 0 and a horizontal asymptote at y = 0.

• The function f(x) = x^(-2) has no asymptotes.

• The function f(x) = x^(-2) approaches y = 1 as x approaches infinity.

Identify the degree of the power function f(x) = 5x^7.

• 7

• 6

• 8

• 5

Solve for x in the equation 4x^2 = 16.

• x = 1

• x = 0

• x = 2 or x = -2

• x = 4

Apply the transformation: f(x) = -x^3 + 2.

• f(x) = -x^2 + 2 transforms x values into new y values.

• f(x) = -x^3 + 2 transforms x values into new y values.

• f(x) = -2x^3 + 2 transforms x values into new y values.

• f(x) = x^3 + 2 transforms y values into new x values.