Transformations of Functions

Front

What is the domain of the function f(x) = x^2?

Back

(-∞, ∞)

Front

Identify the transformation from f(x) = x^2 to g(x) = -(x + 5)^2.

Back

Shifted left 5 units and reflected in the x-axis.

Front

If f(x) = √x, what is g(x) if it is reflected in the x-axis?

Back

g(x) = -√x

Front

What is the equation for g(x) if it is the same as f(x) = x^2 but shifted down 3 units?

Back

g(x) = x^2 - 3

Front

Which equation describes the transformation of shifting f(x) = x^3 four units down?

Back

g(x) = x^3 - 4

Front

What is a vertical reflection of the function f(x) = x^2?

Back

g(x) = -x^2

Front

What does a horizontal shift to the right by 3 units look like for f(x) = x^2?

Back

g(x) = (x - 3)^2

Front

What is the effect of multiplying f(x) = x^2 by 3?

Back

Vertical stretch by a factor of 3: g(x) = 3x^2

Front

What is the transformation of f(x) = x^2 to g(x) = (x + 2)^2 + 1?

Back

Shifted left 2 units and up 1 unit.

Front

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

Back

[1, ∞) because the expression under the square root must be non-negative.