Understanding the Function f(x) = -2√x + 1

The video tutorial explains how to determine the domain of a function, specifically f(x) = -2√x + 1, and how to use a graphing calculator to plot points and graph the function. It covers selecting appropriate X values, inputting the function into the calculator, and verifying the graph. The tutorial also discusses transformations of the square root function, including reflection, vertical stretch, and vertical shift.

What is the domain of the function f(x) = -2√x + 1?

• All real numbers

• x ≥ 0

• x ≤ 0

• x > 0

Why can't x be negative in the function f(x) = -2√x + 1?

• Because the square root of a negative number is not real

• Because it would make the function zero

• Because it would result in a complex number

• Because it would make the function undefined

What is the first step in using a graphing calculator to graph the function?

• Press GRAPH

• Press Y EQUALS and clear old functions

• Press 2nd WINDOW

• Press 2nd GRAPH

Which x values are chosen to simplify the calculation of f(x) = -2√x + 1?

• Any values

• Prime numbers

• Only even numbers

• Perfect squares

What is the y-value when x = 4 for the function f(x) = -2√x + 1?

• -5

• -1.8

• -2.5

• -3

How many points are plotted to create a graph of the function?

• Two points

• Three points

• Four points

• Five points

What does the negative sign in -2√x + 1 indicate about the graph?

• It compresses the graph vertically

• It stretches the graph horizontally

• It reflects the graph across the x-axis

• It shifts the graph up

What transformation is applied by the coefficient 2 in the function f(x) = -2√x + 1?

• Vertical stretch

• Vertical compression

• Horizontal stretch

• Horizontal compression

What does the +1 in the function f(x) = -2√x + 1 represent?

• A vertical shift up

• A vertical shift down

• A horizontal shift

• No shift

If a point (x, y) is on the basic square root function, what is the corresponding point on the transformed function?

• (x, 2y - 1)

• (x, -2y + 1)

• (x, y + 1)

• (x, -2y)