Graphing the Function f(x) = √(0.5x - 1)

The video tutorial explains how to graph the function f(x) = √(0.5x - 1) by sampling x values within its domain. It emphasizes choosing x values that result in integer outputs for easier graphing. The tutorial covers calculating f(x) for selected x values, understanding domain restrictions, and plotting these points to visualize the function's curve. The graph resembles half of a sideways parabola, and the domain is restricted to x ≥ 0.

What is the first step in graphing the function f(x) = √(0.5x - 1)?

• Find the maximum and minimum points.

• Determine the asymptotes.

• Sample some x values within the domain.

• Calculate the derivative of the function.

Tags

CCSS.HSA-REI.B.4B

Why do we choose x values such that 0.5x is a perfect square?

• To ensure f(x) results in clean integers.

• To find the function's asymptotes.

• To simplify the derivative calculation.

• To make the graph symmetrical.

Tags

CCSS.HSF.IF.A.2

What is the value of f(2) for the function f(x) = √(0.5x - 1)?

• -1

• 2

• 0

• 1

What is the domain of the function f(x) = √(0.5x - 1)?

• x ≤ 0

• All real numbers

• x ≥ 0

• x > 0

Why is it important to understand the domain of the function f(x) = √(0.5x - 1)?

• To know which x values will result in real numbers.

• To calculate the function's integral.

• To find the function's maximum value.

• To determine the range of the function.

Tags

CCSS.HSF.IF.A.2

What is the y-coordinate of the point when x = 8 for the function f(x) = √(0.5x - 1)?

• 3

• 2

• 1

• 0

Tags

CCSS.HSF-IF.C.7E

What is the significance of plotting the points on the graph?

• To calculate the function's integral.

• To find the function's derivative.

• To visualize the function's behavior.

• To determine the function's asymptotes.

Tags

CCSS.HSF.IF.A.2

What is the value of f(50) for the function f(x) = √(0.5x - 1)?

• 4

• 6

• 3

• 5

Tags

CCSS.HSF-IF.C.7B

What shape does the graph of the function f(x) = √(0.5x - 1) resemble?

• A circle

• Half of a sideways parabola

• A straight line

• A full parabola

What happens if you pick any x value greater than or equal to 0 for the function f(x) = √(0.5x - 1)?

• It will be negative.

• It will be undefined.

• It will lie on the curve.

• It will not lie on the curve.