Graphs of radical functions

Front

What is the parent function of radical functions?

Back

The parent function of radical functions is f(x) = √x.

Front

What does a vertical stretch by a factor of 2 do to the graph of f(x) = √x?

Back

A vertical stretch by a factor of 2 multiplies the output of the function by 2, making the graph steeper.

Front

How does translating the graph of f(x) = √x down 5 units affect its position?

Back

Translating the graph down 5 units shifts the entire graph downward by 5 units on the y-axis.

Front

What transformations occur when the graph of f(x) = √x is shifted right 2 units?

Back

Shifting right 2 units translates the graph to the right along the x-axis, changing the function to f(x) = √(x - 2).

Front

What does reflecting the graph of f(x) = √x over the x-axis do?

Back

Reflecting over the x-axis inverts the output values, changing the function to f(x) = -√x.

Front

What is the effect of shifting the graph of f(x) = √x up 3 units?

Back

Shifting the graph up 3 units moves the entire graph upward by 3 units on the y-axis, changing the function to f(x) = √x + 3.

Front

Which graph represents the square root parent function?

Back

The graph of f(x) = √x is a curve that starts at the origin (0,0) and increases gradually.

Front

What is the domain of the parent function f(x) = √x?

Back

The domain of f(x) = √x is [0, ∞), meaning x must be greater than or equal to 0.

Front

What is the range of the parent function f(x) = √x?

Back

The range of f(x) = √x is [0, ∞), meaning the output values are also greater than or equal to 0.

Front

How do you identify transformations from the equation of a radical function?

Back

Transformations can be identified by examining changes in the function's equation, such as shifts, stretches, and reflections.