$$(f + g)(x) = x^2$ + x + 1$$, \text{ domain: } (-\infty, \infty)$

$$(g \circ f)(x) = \sqrt{x^2$}$$, \text{ domain: } (-\infty, \infty)$

$$\frac{x^2$}{x-2}$$, \text{ domain: } x \neq 2$

Question 1

Given $$f(x) = x^2$ + 3$$ and $$g(x) = x - 2$$, what is $$(f + g)(x)$$ and its domain?

Accepted Answer

$$(f + g)(x) = x^2$ + x + 1$$, 	ext{ domain: } (-\infty, \infty)$

Question 2

If $$f(x) = x^2$ and g(x$$) = \sqrt{x}$$, what is the domain of (f$$ \circ g)(x)$$?

Accepted Answer

$$[0, \infty)$$

Question 3

Given $$f(x) = x + \frac{1}{x}$$ and $$g(x) = \frac{x+1}{x+2}$$, which value is NOT in the domain of $$(f \circ g)(x)$$?

Accepted Answer

$$x = -2$$

Question 4

Which transformation will shift the graph of $$f(x) to $$the right by 3 units?

Accepted Answer

$$f(x-3)$$

Question 5

If $$f(x) = x^2$ and g(x) = x + 1$, what is (f$$ \cdot g)(x)$$?

Accepted Answer

$$(f \cdot g)(x) = x^2$(x + 1)$$

Question 6

Which of the following represents a vertical stretch of $$f(x) by a $$factor of 2?

Accepted Answer

$$2f(x)$$

Question 7

Given $$f(x) = x^2$ and g(x$$) = \sqrt{x}$$, what is (g$$ \circ f)(x)$$ and its domain?

Accepted Answer

$$(g \circ f)(x) = \sqrt{x^2$}$$, 	ext{ domain: } (-\infty, \infty)$

Question 8

Which transformation reflects the graph of $$f(x)$$ about the $$x-$$axis?

Accepted Answer

$$-f(x)$$

Question 9

If $$f(x) = x^2$ and g(x) = x + 1$, what is (f - g)(x$$)$$?

Accepted Answer

$$(f - g)(x) = x^2$ - x - 1$$

Question 10

Given $$f(x) = x^2$ and g(x) = x - 2$, what is $$\left(\frac{f}{g}\right)(x)$$ and its domain?

Accepted Answer

$$\frac{x^2$}{x-2}$$, 	ext{ domain: } x 
eq 2$

Question 11

Which transformation will shift the graph of $$f(x) up by 4 $$units?

Accepted Answer

$$f(x) + 4$$

Question 12

If $$f(x) = x^2$ and g(x$$) = \sqrt{x}$$, what is the domain of (f$$ \circ g)(x)$$?

Accepted Answer

$$[0, \infty)$$

Question 13

Given $$f(x) = x^2$ and g(x) = x + 1$, what is (g$$ \circ f)(x)$$?

Accepted Answer

$$(g \circ f)(x) = x^2$ + 1$$

Question 14

Which transformation compresses the graph of $$f(x)$$ vertically by a factor of $$\frac{1}{3}$$?

Accepted Answer

$$\frac{1}{3}f(x)$$

Question 15

If $$f(x) = x^2$ and g(x) = x + 1$, what is (f$$ \circ g)(x)$$?

Accepted Answer

$$(f \circ g)(x) = (x + 1)^2$

Combining Functions, Shifting, and Scaling Graphs

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