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Section 1-1 : Review : Functions

1. Perform the indicated function evaluations for $$f\left( x \right) = 3 - 5x - 2{x^2}$$.

1. $$f\left( 4 \right)$$
2. $$f\left( 0 \right)$$
3. $$f\left( { - 3} \right)$$
1. $$f\left( {6 - t} \right)$$
2. $$f\left( {7 - 4x} \right)$$
3. $$f\left( {x + h} \right)$$

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a $$f\left( 4 \right)$$ Show Solution
$f\left( 4 \right) = 3 - 5\left( 4 \right) - 2{\left( 4 \right)^2} = - 49$

b $$f\left( 0 \right)$$ Show Solution
$f\left( 0 \right) = 3 - 5\left( 0 \right) - 2{\left( 0 \right)^2} = 3$

c $$f\left( { - 3} \right)$$ Show Solution
$f\left( { - 3} \right) = 3 - 5\left( { - 3} \right) - 2{\left( { - 3} \right)^2} = 0$

Hint : Don’t let the fact that there are now variables here instead of numbers get you confused. This works exactly the same way as the first three it will just have a little more algebra involved.
d $$f\left( {6 - t} \right)$$ Show Solution
\begin{align*}f\left( {6 - t} \right) & = 3 - 5\left( {6 - t} \right) - 2{\left( {6 - t} \right)^2}\\ & = 3 - 5\left( {6 - t} \right) - 2\left( {36 - 12t + {t^2}} \right)\\ & = 3 - 30 + 5t - 72 + 24t - 2{t^2}\\ & = - 99 + 29t - 2{t^2}\end{align*}

Hint : Don’t let the fact that there are now variables here instead of numbers get you confused. This works exactly the same way as the first three it will just have a little more algebra involved.
e $$f\left( {7 - 4x} \right)$$ Show Solution
\begin{align*}f\left( {7 - 4x} \right) & = 3 - 5\left( {7 - 4x} \right) - 2{\left( {7 - 4x} \right)^2}\\ & = 3 - 5\left( {7 - 4x} \right) - 2\left( {49 - 56x + 16{x^2}} \right)\\ & = 3 - 35 + 20x - 98 + 112x - 32{x^2}\\ & = - 130 + 132x - 32{x^2}\end{align*}

Hint : Don’t let the fact that there are now variables here instead of numbers get you confused. Also, don’t get excited about the fact that there is both an $$x$$ and an $$h$$ here. This works exactly the same way as the first three it will just have a little more algebra involved.
f $$f\left( {x + h} \right)$$ Show Solution
\begin{align*}f\left( {x + h} \right) & = 3 - 5\left( {x + h} \right) - 2{\left( {x + h} \right)^2}\\ & = 3 - 5\left( {x + h} \right) - 2\left( {{x^2} + 2xh + {h^2}} \right)\\ & = 3 - 5x - 5h - 2{x^2} - 4xh - 2{h^2}\end{align*}