Transformation of graphs HW

Front

What are the transformations in the function y=(x-2)^3 + 4?

Back

Horizontal shift right 2 units and vertical shift up 4 units.

Front

Which function represents a vertical stretch of the parent function f(x)=x^2?

Back

g(x) = 2x^2.

Front

What is the parent function of the absolute value function?

Back

The parent function is the absolute value function itself, denoted as f(x) = |x|.

Front

Which function does NOT represent a horizontal shift of f(x)=x^2?

Back

g(x) = x^2 + 3.

Front

What transformation occurs when f(x) = x is replaced with 2f(x)?

Back

Vertical stretch by a factor of 2.

Front

What does a horizontal shift to the left by 3 units look like in function notation?

Back

g(x) = f(x + 3).

Front

What is the effect of a vertical translation down by 5 units on the function f(x)?

Back

g(x) = f(x) - 5.

Front

How does the graph of g(x) = (x - 1)^2 compare to f(x) = x^2?

Back

It is shifted right by 1 unit.

Front

What is the effect of multiplying a function by a negative number?

Back

It reflects the graph across the x-axis.

Front

What transformation occurs when the function f(x) = x^2 is replaced with f(x) = (1/2)x^2?

Back

Vertical compression by a factor of 1/2.