Question

The graph of $y=f\left(x\right)$ is given. Match each equation with its graph

1. $y=f(x-4)$
2. $y=f\left(x\right)+3$
3. $y=2f(x+6)$
4. $y=-f\left(2x\right)$

Short answer

1. $y=f(x-4)$is graph 3.
2. $y=f\left(x\right)+3$is graph 1.
3. $y=2f(x+6)$is graph 2.
4. $y=-f\left(2x\right)$ is graph 4.

Step-by-step solution

Step 1. Concept of Horizontal shift, vertical shift, reflection in x or y axis, vertical stretching.

To graph $y=f(x-c)$, shifts the graph$y=f\left(x\right)$ to the right c units

And, to graph$y=f(x+c)$ shifts the graph$y=f\left(x\right)$ to the left c units

To graph$y=cf\left(x\right)$

If $c>1$; stretch the graph of$y=f\left(x\right)$ vertically by a factor of c

Step 2. Identifying the graph from equations.

$y=f(x-4)$

In this graph the function f shifts 4 units right

$y=f\left(x\right)+3$

In this graph the function f shifts 3 units upward

$y=2f(x+6)$

In this graph the function f stretch vertically by a factor of 2 and shift 6 unit left.

$y=-f\left(2x\right)$

In this graph the function f reflect in the x axis and shrink vertically by a factor of$\frac{1}{2}$

Step 3. Matching the equation from the graph.

1. $y=f(x-4)$is graph 3.
2. $y=f\left(x\right)+3$is graph 1.
3. $y=2f(x+6)$is graph 2.
4. $y=-f\left(2x\right)$ is graph 4.