Describe the Transformation h(x)=-3x-4

$h (x) = - 3 x - 4$

The parent function is the simplest form of the type of function given.

$g (x) = x$

Find the y-intercepts.

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The slope-intercept form is $y = m x + b$ , where $m$ is the slope and $b$ is the y-intercept.

$y = m x + b$

Using the slope-intercept form, find the y-intercept for $g (x) = x$ .

$b_{1} = 0$

Using the slope-intercept form, find the y-intercept for $h (x) = - 3 x - 4$ .

$b_{2} = - 4$

List the y-intercepts.

$b_{1} = 0$

$b_{2} = - 4$

$b_{1} = 0$

$b_{2} = - 4$

The vertical shift depends on the y-intercept value $b$ , where $b = b_{2} - b_{1}$

$b_{2} - b_{1} = - 4$

Since $b < 0$ , the graph is shifted down $4$ units.

Shifted down $4$ units

Find the slopes.

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The slope-intercept form is $y = m x + b$ , where $m$ is the slope and $b$ is the y-intercept.

$y = m x + b$

Using the slope-intercept form, find the slope for $g (x) = x$ .

$m_{1} = 1$

Using the slope-intercept form, find the slope for $h (x) = - 3 x - 4$ .

$m_{2} = - 3$

List the slopes.

$m_{1} = 1$

$m_{2} = - 3$

$m_{1} = 1$

$m_{2} = - 3$

The vertical stretch depends on the slope.

If $| m_{2} | < | m_{1} |$ , vertical compression

If $| m_{2} | > | m_{1} |$ , vertical stretch

If $| m_{2} | = | m_{1} |$ , no vertical stretch or compression.

Since $| m_{2} | > | m_{1} |$ , the graph is vertically stretched.

Vertical stretch

Since $m_{1}$ and $m_{2}$ have opposite signs, the graph is reflected about the y-axis.

Reflected about the y-axis

Describe the transformation from the function $g (x) = x$ .

Shifted down $4$ units

Vertical stretch

Reflected about the y-axis

Describe the Transformation h(x)=-3x-4

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