Difference between revisions of "Week2a"
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== Extra discussion questions == | == Extra discussion questions == | ||
| + | # Find a constant $k$ such that the line through the points $(k,2)$ and $(3,6)$ has the same rate of change as the line $y=4x+3$. | ||
| + | # Graphically determine the $x$-values for which $\frac{2}{5}x+7>3$. | ||
| + | # Suppose that a bar charges a \$8 cover fee upon entry and \$4.75 per drink. Write a linear equation representing your cost for a night out in terms of how many drinks you ordered. | ||
# Find the number $c$ such that $x^2+5x+c$ is a perfect square for all $x$ values. | # Find the number $c$ such that $x^2+5x+c$ is a perfect square for all $x$ values. | ||
| − | # Determine the $x$-values for which $x^2+4x+1\geq 1$. | + | # Determine the $x$-values for which $x^2+4x+1\geq 1$. How would you solve this graphically? |
| − | + | ||
Revision as of 15:10, 3 November 2014
Handouts
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 $100^{\circ}C = 212^{\circ}F$.
- Write a linear equation expressing $F$ in terms of $C$ and sketch its graph.
- If it is $75^{\circ}C$, what is the temperature in $F$?
- If it is $75^{\circ}F$, what is the temperature in $C$?
- What about if it is $175^{\circ}F$?
- What about if it is $-25^{\circ}F$?
- Did you compute each $C$ in parts (3) - (5) separately? Could you have avoided this?
- 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
- Find a constant $k$ such that the line through the points $(k,2)$ and $(3,6)$ has the same rate of change as the line $y=4x+3$.
- Graphically determine the $x$-values for which $\frac{2}{5}x+7>3$.
- Suppose that a bar charges a \$8 cover fee upon entry and \$4.75 per drink. Write a linear equation representing your cost for a night out in terms of how many drinks you ordered. # Find the number $c$ such that $x^2+5x+c$ is a perfect square for all $x$ values. # Determine the $x$-values for which $x^2+4x+1\geq 1$. How would you solve this graphically?
