Thread: Need help with Calculus Packet

1. Need help with Calculus Packet

I have a calculus packet to do over the summer. I did as much as i could but i really didn't know how to do a few questions.

1. Find a formula for the function f graphed below
(theres a graph with the points (0,0)(1,1)(2,0)(3,0)(4,0)(5,0)

2. Let f and g be odd functions. If p,r, and s are nonzero functions defined as follows, which must be odd?
I. p(x)=f(g(x)) II. r(x)=f(x)+g(x) III. s(x)=f(x)*g(x)
(A) I only; (B) II only; (C) I and II only; (D) II and III only; (E) I, II, and III

3. The graphs of f and g are shown below and h=f º g. Estimate the value of h(0.5). Then sketch the value of h

Any help is greatly appreciated

2. Originally Posted by sanghoon93
3. The graphs of f and g are shown below and h=f º g. Estimate the value of h(0.5). Then sketch the value of h

Any help is greatly appreciated
$\displaystyle h(x)=(f \circ g)(x)=f(g(x))$

So to evaluate $\displaystyle h(0.5)$ look up the value of $\displaystyle g(0.5)$ and lets call that $\displaystyle u$, then look up $\displaystyle f(u).$

CB

3. Originally Posted by sanghoon93
2. Let f and g be odd functions. If p,r, and s are nonzero functions defined as follows, which must be odd?

I. p(x)=f(g(x))

II. r(x)=f(x)+g(x)

III. s(x)=f(x)*g(x)

(A) I only; (B) II only; (C) I and II only; (D) II and III only; (E) I, II, and III
The defining property for a function $\displaystyle h(x)$ to be odd is that $\displaystyle h(-x)=-h(x)$.

Now for each of the given functions you need to determine if this property holds. I will do I. for you:

$\displaystyle p(x)=f(g(x))$

so:

$\displaystyle p(-x)=f(g(-x))$

but $\displaystyle g$ is odd so $\displaystyle g(-x)=-g(x)$ hence:

$\displaystyle p(-x)=f(-g(x))$

but $\displaystyle f$ is also odd so:

$\displaystyle p(-x)=-f(g(x))=-p(x)$

and so $\displaystyle p$ is odd.

CB