Understanding Function Transformations

f(x) = -x

f(x) = x^2

f(x) = x

f(x) = 2x

g(x) = 2 * f(x)

g(x) = f(x) + 2

g(x) = -f(x)

g(x) = -2 * f(x)

-3

3

6

-6

It flips over the x-axis and scales by a factor of 2.

It shifts up by 2 units.

It remains unchanged.

It shifts down by 2 units.

It shifts the graph downwards.

It makes the graph narrower.

It flips the graph over the x-axis.

It shifts the graph to the left.

h(x) = f(3x)

h(x) = f(x/3)

h(x) = f(1/3 * x)

h(x) = 3 * f(x)

1

6

2

3

It makes the graph narrower.

It shifts the graph to the right.

It makes the graph wider.

It flips the graph over the y-axis.

-9

9

-3

3

It makes the graph wider.

It makes the graph narrower.

It flips the graph over the x-axis.

It shifts the graph upwards.