What is the effect of a negative coefficient in front of a function?

A negative coefficient, such as in $$g(x) = -f(x)$$ , reflects the graph across the x-axis.

What does the equation $$y = f(x - 4)$$ represent?

The equation $$y = f(x - 4)$$ represents a horizontal shift of the graph of $$f(x)$$ to the right by 4 units.

What does the equation $$y = f(x) + 2$$ represent?

The equation $$y = f(x) + 2$$ represents a vertical shift of the graph of $$f(x)$$ upward by 2 units.

What is the effect of the transformation $$g(x) = 3f(x)$$ ?

The transformation $$g(x) = 3f(x)$$ vertically stretches the graph of $$f(x)$$ by a factor of 3.

What does the equation $$g(x) = \frac{1}{3}f(x)$$ represent?

The equation $$g(x) = \frac{1}{3}f(x)$$ represents a vertical compression of the graph of $$f(x)$$ by a factor of 1/3.

What is a translation in the context of function transformations?

A translation is a type of transformation that shifts the graph of a function horizontally or vertically without changing its shape.

What is the difference between a vertical stretch and a vertical compression?

A vertical stretch occurs when the output values of a function are multiplied by a factor greater than 1, making the graph taller. A vertical compression occurs when the output values are multiplied by a factor between 0 and 1, making the graph shorter.

How do you identify the transformation from the equation $$y = f(x) + c$$ ?

In the equation $$y = f(x) + c$$ , the graph of $$f(x)$$ is shifted vertically. If $$c > 0$$ , it shifts up; if $$c

Transformations of Linear Functions Flashcards

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