Week2a

Handouts

Handout on linear functions Handout on quadratic functions

Activities

Activity: working with linear functions.

The temperature scales Celsius and Fahrenheit have a linear relationship with $0^{\circ}C = 32^{\circ}F$ and $100^{\circ}C = 212^{\circ}F$.

1. Write a linear equation expressing $F$ in terms of $C$ and sketch its graph.
2. If it is $75^{\circ}C$, what is the temperature in $F$?
3. If it is $75^{\circ}F$, what is the temperature in $C$?
4. What about if it is $175^{\circ}F$?
5. What about if it is $-25^{\circ}F$?
6. Did you compute each $C$ in parts (3) - (5) separately? Could you have avoided this?
7. Graph the line $F=C$ on the same axes. Can you tell from your graph if there a temperature $x$ for which $x^{\circ}C=x^{\circ}F$? If so, what is $x$?

Activity: working with quadratic functions.

The revenue of Miley Cyrus' concert in Vancouver depends on the number of unsold seats. Miley's manager calculates that the revenue is given by $R(x) = 8000+70x-x^2$, where $x$ is the number of unsold seats. Find the maximum revenue and the number of unsold seats that corresponds to maximum revenue.

Activity: working with general functions.

Consider the following table of function values for $f(x)$ and $g(x)$.

a) Evaluate: $(f+g)(4)$, $\dfrac{f}{g}(3)$, $\dfrac{g}{f}(3)$, $(f\cdot g)(5)$, $(f\circ g)(5)$, $(g\circ f)(2)$, $f^{-1}(-3)$, $g^{-1}(8)$.

b) Suppose $f$ is even and $g$ is odd. Evaluate $f(-3)$ and $g(-5)$.

Extra discussion questions

1. Find the number $c$ such that $x^2+5x+c$ is a perfect square for all $x$ values.
2. Determine the $x$-values for which $x^2+4x+1\geq 1$.
3. What are the $x$-intercepts of $y=x^2-4x+5$? Justify your answer.