Calculus I - Week 01 Homework

Problems

Problem 01-01 - Written HW, Monday Gradescope - from WebAssign §1.1-06

01

Compute difference quotient

Suppose $f(x)=-x^3$. Compute and simplify the difference quotient: $$\frac{f(a+h)-f(a)}{h}$$

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Problem 01-02 - Written HW, Monday Gradescope - new problem

02

Domains of funny functions

Consider the following functions:

• (a) $f(x)=\sqrt{3-x}+\sqrt{4+x}$
• (b) $f(x)=\frac{x+1}{1+\frac{1}{1+x}}$

What is the largest possible domain for each of these functions?

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Problem 01-03 - Presentation, Tuesday - new problem

03

Piecewise function from graph

Find the piecewise formula for the function with this graph:

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Problem 01-04 - Presentation, Tuesday - partly from WebAssign §1.1-15

04

Even v Odd for a product function

• (a) Consider the function $f(x)=x|x|$. Is it even or odd?
• (b) If $f(x)$ is even/odd and $g(x)$ is even/odd, what is $f\cdot g$? (There are four separate cases to describe.)

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