Operations INSIDE vs OUTSIDE of Functions

INSIDE the Function vs OUTSIDE the Function

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Function Notation

f(x) is the same as y

g(x) is the same as y

h(x) is the same as y

Fill in the Blanks

f(x) is the same as

Fill in the Blanks

g(x) is the same as

Fill in the Blanks

h(x) is the same as

Multiple Select

Check all that are correct.

f(x) = x + 3 is the same as

• x = x + 3

• y = x + 3

• y = 1x + 3

• y = 3 + x

• y = 3 - x

INSIDE the function vs. OUTSIDE the function

Examples of adding INSIDE the function

Multiple Select

Which equations have addition INSIDE the function? Select that apply.

• $$f\left(x\right)=\sqrt{x+3}$$

• $$f\left(x\right)=\sqrt{x}+2$$

• $$f\left(x\right)=\left(x+8\right)^2$$

• $$f\left(x\right)=x^2+7$$

• $$f\left(x\right)=\left|x\right|+3$$

Multiple Select

Which equations have addition INSIDE the function? Select that apply.

• $$f\left(x\right)=^{\ 3}\sqrt{x+5}$$

• $$f\left(x\right)=4\sqrt{x}$$

• $$f\left(x\right)=\left(x+9\right)^3$$

• $$f\left(x\right)=x^3+11$$

• $$f\left(x\right)=\left|x+2\right|$$

Examples of adding OUTSIDE the function

Multiple Select

Which equations have addition OUTSIDE the function? Select that apply.

• $$f\left(x\right)=\sqrt{x+3}$$

• $$f\left(x\right)=\sqrt{x}+2$$

• $$f\left(x\right)=\left(x+8\right)^2$$

• $$f\left(x\right)=x^2+7$$

• $$f\left(x\right)=\left|x\right|+3$$

Multiple Select

Which equations have addition OUTSIDE the function? Select that apply.

• $$f\left(x\right)=^{\ 3}\sqrt{x+5}$$

• $$f\left(x\right)=4\sqrt{x}$$

• $$f\left(x\right)=\left(x+9\right)^3$$

• $$f\left(x\right)=x^3+11$$

• $$f\left(x\right)=\left|x\right|+8$$

Examples of subtracting INSIDE the function

Multiple Select

Which equations have subtraction INSIDE the function? Select that apply.

• $$f\left(x\right)=\sqrt{x-9}$$

• $$f\left(x\right)=\sqrt{x-5}$$

• $$f\left(x\right)=\left(x-4\right)^2$$

• $$f\left(x\right)=x^2+7$$

• $$f\left(x\right)=\left|x-8\right|$$

Multiple Select

Which equations have subtraction INSIDE the function? Select that apply.

• $$f\left(x\right)=^{\ 3}\sqrt{x+5}$$

• $$f\left(x\right)=\sqrt{x-8}$$

• $$f\left(x\right)=\left(x-9\right)^3$$

• $$f\left(x\right)=x^3-11$$

• $$f\left(x\right)=\left|x\right|-3$$

Examples of subtracting OUTSIDE the function

Multiple Select

Which equations have subtraction OUTSIDE of the function?

• $$f\left(x\right)=^{\ 3}\sqrt{x+5}$$

• $$f\left(x\right)=\sqrt{x-8}$$

• $$f\left(x\right)=\left(x-9\right)^3$$

• $$f\left(x\right)=x^3-11$$

• $$f\left(x\right)=\left|x\right|-3$$

Multiple Select

Which equations have subtraction OUTSIDE of the function?

• $$f\left(x\right)=\sqrt{x-9}$$

• $$f\left(x\right)=\sqrt{x}-3$$

• $$f\left(x\right)=\left(x-4\right)^2$$

• $$f\left(x\right)=x^2-7$$

• $$f\left(x\right)=\left|x-8\right|$$

Examples of multiplying INSIDE the function

Multiple Select

Which equations have multiplication INSIDE the function? Select that apply.

• $$f\left(x\right)=5^{\ 3}\sqrt{x}$$

• $$f\left(x\right)=\sqrt{8x}$$

• $$f\left(x\right)=\left(9x\right)^3$$

• $$f\left(x\right)=11x^3$$

• $$f\left(x\right)=\left|-x\right|$$

Multiple Select

Which equations have multiplication INSIDE the function? Select that apply.

• $$f\left(x\right)=9\sqrt{x}$$

• $$f\left(x\right)=\sqrt{9x}$$

• $$f\left(x\right)=\left(7x\right)^2$$

• $$f\left(x\right)=7x^2$$

• $$f\left(x\right)=\left|8x\right|$$

Examples of multiplying OUTSIDE the function

Multiple Select

Which equations have multiplication OUTSIDE the function? Select that apply.

• $$f\left(x\right)=9\sqrt{x}$$

• $$f\left(x\right)=\sqrt{9x}$$

• $$f\left(x\right)=\left(7x\right)^2$$

• $$f\left(x\right)=7x^2$$

• $$f\left(x\right)=-\left|x\right|$$

Multiple Select

Which equations have multiplication OUTSIDE the function? Select that apply.

• $$f\left(x\right)=5^{\ 3}\sqrt{x}$$

• $$f\left(x\right)=\sqrt{8x}$$

• $$f\left(x\right)=\left(9x\right)^3$$

• $$f\left(x\right)=11\left(x\right)^3$$

• $$f\left(x\right)=5\left|x\right|$$