How does the graph of g(x)=x+4 compares with the graph of the parent function, f(x)=x?

Mathematics

1 answer:

irakobra [83]3 years ago

4 0

The graph of g(x) is shifted 4 units up ⇒ answer a

Step-by-step explanation:

Let us revise the translation

If the function f(x) translated horizontally to the right by h units, then its image is g(x) = f(x - h)
If the function f(x) translated horizontally to the left by h units, then its image is g(x) = f(x + h)
If the function f(x) translated vertically up by k units, then its image is g(x) = f(x) + k
If the function f(x) translated vertically down by k units, then its image is g(x) = f(x) - k

∵ The parent function f(x) = x

∵ g (x) = x + 4

- Substitute x in g(x) by f(x)

∴ g(x) = f(x) + 4

- g(x) is f(x) add by 4

- by using the rule of translation above

∵ g(x) = f(x) + k

∵ k = 4

∴ g(x) is the image of f(x) after translation 4 units up

∴ The graph of g(x) is 4 units above the graph of f(x)

The graph of g(x) is shifted 4 units up

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