Question

f(x)=1x−2+4 and g(x)=1x+3+6 . Select from the drop-down menus to correctly complete the statement. You can get the graph of function g by taking the graph of function f and shifting it units to the , and by shifting it units .

Answer 1

You can get the graph of function g by taking the graph of function f and shifting it 7 units to the left, and by shifting it 7 units up.

Explanation:

We have the following functions:

$f(x)=1x-2+4 \\ \\ g(x)=1x+3+6$

But we can rewrite this functions as:

$f(x)=1x-2+4 \rightarrow f(x)=x+2 \\ \\ g(x)=1x+3+6 \rightarrow g(x)=x+9$

Or:

$g(x)=(x+2)+7$

Recall that for vertical shifts:

$h(x)=f(x)+k \\ \\ \bullet \ if \ k>0 \ f(x) \ is \ shifted \ k \ units \ up \\ \\ \bullet \ if \ k$

From this, we know that:

• We can get g(x) by shifting the graph of f(x) 7 units upward

Recall that for horizontal shifts:

$h(x)=f(x+k) \\ \\ \bullet \ if \ k>0 \ f(x) \ is \ shifted \ k \ units \ to \ the \ left \\ \\ \bullet \ if \ k$

From this, we know that:

• We can get g(x) by shifting the graph of f(x) 7 units to the left

Learn more:

Shifting graphs: brainly.com/question/10010217

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