Question

Below is the graph of y= x. Translate it to make it the graph of y= x-1 + 4.

Answer 1

• First, to shift the graph of $y=x$ 1 unit to the right, so $y=x-1$
• Second, to shift the graph of $y=x-1$ 4 units to the left, so $y=x-1+4$

Explanation:

To translate the graph of a function is part of Rigid Transformations because the basic shape of the graph is unchanged

$Let \ c \ be \ a \ positive \ real \ number. \ \mathbf{Vertical \ and \ horizontal \ shifts} \\ in \ the \ graph \ of \ y=f(x) \ are \ represented \ as \ follows:$

$\bullet \ Vertical \ shift \ c \ units \ \mathbf{upward}: \\ h(x)=f(x)+c \\ \\ \bullet \ Vertical \ shift \ c \ units \ \mathbf{downward}: \\ h(x)=f(x)-c$

$\bullet \ Horizontal \ shift \ c \ units \ to \ the \ right \ \mathbf{right}: \\ h(x)=f(x-c) \\ \\ \bullet \ Horizontal \ shift \ c \ units \ to \ the \ left \ \mathbf{left}: \\ h(x)=f(x+c)$

In this case, we have the graph of:

$y=x$

And we need to translate it to make it the graph of:

$y=x-1+4$

According to our rules we need:

• First, to shift the graph of $y=x$ 1 unit to the right, so $y=x-1$
• Second, to shift the graph of $y=x-1$ 4 units to the left, so $y=x-1+4$

But $y=x-1+4$ is the same as $y=x+3$, so the previous steps can be simplified as:

• Shifting the graph of $y=x$ 3 unit to the left.

Below are shown those graphs:

• The blue one is $y=x$
• The red one is $y=x-1+4$

Learn more:

Shifting graphs: brainly.com/question/10010217

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