Function Transformations

Front

What is a transformation in the context of function graphs?

Back

A transformation refers to the changes made to the graph of a function, which can include shifts, stretches, compressions, and reflections.

Front

What does a horizontal shift to the right by 'h' units look like in function notation?

Back

g(x) = f(x - h) where h > 0.

Front

What does a vertical shift up by 'k' units look like in function notation?

Back

g(x) = f(x) + k where k > 0.

Front

How does a reflection over the x-axis affect the function?

Back

It changes the sign of the output, resulting in g(x) = -f(x).

Tags

CCSS.HSF.BF.B.3

Front

What is the effect of a vertical stretch by a factor of 'a'?

Back

It multiplies the output of the function by 'a', resulting in g(x) = a*f(x) where a > 1.

Front

What does a vertical compression by a factor of 'b' mean?

Back

It reduces the output of the function by a factor of 'b', resulting in g(x) = (1/b)*f(x) where 0 < b < 1.

Front

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

Back

g(x) = f(x + h) where h > 0.

Front

How do you represent a reflection over the y-axis in function notation?

Back

g(x) = f(-x).

Front

What is the transformation represented by g(x) = f(x - 3) + 5?

Back

Shifted right 3 units and up 5 units.

Tags

CCSS.HSF.BF.B.3

Front

What transformations are represented by g(x) = -f(x + 6) - 10?

Back

Reflected over the x-axis, shifted left 6 units, and shifted down 10 units.

Tags

CCSS.HSF.BF.B.3