(Solved): 1. The superposition principle applies when you have two functions, $$f(x)$$ and $$g(x)$$, and ...

1. The superposition principle applies when you have two functions, $$f(x)$$ and $$g(x)$$, and you are trying to obtain the graph of a. $$y=f(x)+g(x)$$ b. $$y=\frac{f(x)}{g(x)}$$ c. $$y=f(x) g(x)$$ d. $$y=f(g(x))$$ 2. Given the functions $$f(x)=x^{2}+1$$ and $$g(x)=3-x$$, determine an equation for the combined function $$y=f(x)+g(x)$$. a. $$y=x^{2}-x+2$$ b. $$y=x^{2}-x+4$$ c. $$y=x^{2}+x+4$$ d. $$y=x^{2}+x-2$$ 3. Given the functions $$f(x)=x^{2}+1$$ and $$g(x)=3-x$$, determine an equation for the combined function $$y=f(x) g(x)$$. a. $$y=-x^{3}+3 x^{2}-x+3$$ b. $$y=-x^{3}+3 x^{2}+x-3$$ c. $$y=x^{3}+3 x^{2}-x+3$$ d. $$y=-x^{3}+2 x^{2}-x+3$$ 4. Given the functions $$f(x)=x^{3}-x$$ and $$g(x)=x-1$$, determine an cquation for the combined function $$y=\frac{f(x)}{g(x)}$$. a. $$y=x^{2}+x, x \neq 1$$ b. $$y=\frac{x}{x-1}, x \neq 1$$ c. $$y=x^{2}-x, x \neq 1$$ d. $$y=\frac{x^{2}-x}{x-1}, x=1$$ 5. Given the functions $$f(x)=x^{2}-x$$ and $$g(x)=x-1$$, determine an equation for the composite function $$y=f(g(x))$$. a. $$y=x^{2}-3 x+1$$ b. $$y=x^{2}-3 x+2$$ c. $$y=x^{2}-x-1$$ d. $$y=x^{2}-x+1$$ 6. Given the functions $$f(x)=\sin x$$ and $$g(x)=x$$, determine the domain of the combined function $$y=f(x)+g(x)$$. a. $$\{x \in \mathbb{R},-2 \pi \leq x \leq 2 \pi\}$$ b. $$\{x \in \mathbb{R}\}$$ c. $$\{x \in \mathbb{R},-1 \leq x \leq 1\}$$ d. cannot be determined 7. In general, the zeros of a function $$f(x)$$ appear on the graph of $$y=f(x) g(x)$$ as $$A x$$-intercepts b.holes c. vertical asymptotes d. local extreme points 8. The zeros of a function $$g(x)$$ appear on the graph of $$y=\frac{f(x)}{g(x)}$$ as a. $$x$$-intercepts b. holes c. vertical asymptotes d. B or $$\mathrm{C}$$

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