warm-up.md

1. Calculate images and counterimages

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$f$ defined on $\reals$ by $f(x)=3x-1$

1. Image of 5:

$$f(5)=3\times{5}-1=14$$

2. Calculate $f(-1)$

$$f(-1) = 3\times-1-1=-4$$

3. Counter images of 8

$$f(x) = 3x - 1 = 8$$

$$3x = 9$$

$$x = 3$$

2. Give expression based on unknown

$f$ defined on $\reals$ by $f(x)=x^2-1$

1. Give $f(n+1)$ based on n

$$f(n+1) = (n+1)^2 - 1$$

$$f(n+1) = n^2 + 2n$$

2. Give $f(n-1)$ based on n

$$f(n-1) = (n-1)^2 - 1$$

$$f(n-1) = n^2 - 2n$$

3. Give $f(2n)$ based on n

$$f(2n) = 4n^2 - 1$$

3. Calculate with powers

$$A=2^4\times2^3 = 2^7$$

$$B=\frac{2^6}{2^2} = 2^4$$

$$C=(2^-1)^3 = 2^{-3}$$