Exploring Power Functions

Evaluate: What is 2^3?

• 4

• 6

• 8

• 10

Evaluate: What is 3^2?

• 12

• 15

• 9

• 6

Graph the function f(x) = x^2. What shape do you see?

• The shape is a triangle.

• The shape is a straight line.

• The shape is a parabola.

• The shape is a circle.

Graph the function f(x) = x^3. Describe its appearance.

• The graph of f(x) = x^3 is a U-shaped curve that opens upwards.

• The graph of f(x) = x^3 is an S-shaped curve that passes through the origin, symmetric about the origin, rising steeply in the first quadrant and falling steeply in the third quadrant.

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

• The graph of f(x) = x^3 is a straight line that passes through the origin.

Identify the transformation: f(x) = (x - 2)^2. What is shifted?

• The graph is shifted 2 units down.

• The graph is shifted 2 units up.

• The graph is shifted 2 units to the left.

• The graph is shifted 2 units to the right.

Identify the transformation: f(x) = -x^2. How does it change the graph?

• The graph is reflected across the x-axis.

• The graph is stretched vertically.

• The graph is shifted to the right.

• The graph is rotated 90 degrees.

Evaluate: What is 4^0?

• 16

• 4

• 1

• 0

Evaluate: What is 5^1?

• 10

• 25

• 5

• 1

Graph the function f(x) = 2x^2. How does it compare to f(x) = x^2?

• f(x) = 2x^2 is a horizontal stretch of f(x) = x^2, making it wider.

• f(x) = 2x^2 is a vertical stretch of f(x) = x^2, making it narrower.

• f(x) = 2x^2 is identical to f(x) = x^2, with no changes.

• f(x) = 2x^2 is a reflection of f(x) = x^2 across the x-axis.

Identify the transformation: f(x) = x^2 + 3. What happens to the graph?

• The graph is stretched vertically by a factor of 3.

• The graph is shifted upwards by 3 units.

• The graph is shifted downwards by 3 units.

• The graph is reflected over the x-axis.