Algebra Examples

$f (x) = x^{2} + 2$ , $g (x) = x^{2} + 5$

Step 1

The transformation being described is from $f (x) = x^{2} + 2$ to $g (x) = x^{2} + 5$ .

$f (x) = x^{2} + 2 \to g (x) = x^{2} + 5$

Step 2

The horizontal shift depends on the value of $h$ . The horizontal shift is described as:

$g (x) = f (x + h)$ - The graph is shifted to the left $h$ units.

$g (x) = f (x - h)$ - The graph is shifted to the right $h$ units.

In this case, $h = 0$ which means that the graph is not shifted to the left or right.

Horizontal Shift: None

Step 3

The vertical shift depends on the value of $k$ . The vertical shift is described as:

$g (x) = f (x) + k$ - The graph is shifted up $k$ units.

$g (x) = f (x) - k$ - The graph is shifted down $k$ units.

Vertical Shift: Up $3$ Units

Step 4

The graph is reflected about the x-axis when $g (x) = - f (x)$ .

Reflection about the x-axis: None

Step 5

The graph is reflected about the y-axis when $g (x) = f (- x)$ .

Reflection about the y-axis: None

Step 6

Compressing and stretching depends on the value of $a$ .

When $a$ is greater than $1$ : Vertically stretched

When $a$ is between $0$ and $1$ : Vertically compressed

Vertical Compression or Stretch: None

Step 7

Compare and list the transformations.

Horizontal Shift: None

Vertical Shift: Up $3$ Units

Reflection about the x-axis: None

Reflection about the y-axis: None

Vertical Compression or Stretch: None

Step 8