4.2E: Exercises

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Evaluate functions

For the function $f(x)=5x^2−8x+1$ find $f(1)$
For the function $f(x)=x^3+2x-1$ find $f(0)$
For the function $f(x)=-3x^4−2x+3$ find $f(-2)$
For the function $f(x)=8x+6$ find $f(-3)$
For the function $f(x)=x^2+1$ find $f(-10)$

Answer

-2
-1
-41
-18
101

Application to evaluating functions

The polynomial function $h(t)=−16t^2+300$ gives the height of a ball t seconds after it is dropped from a 100-foot tall bridge. Find the height after $t=3$ seconds.
The polynomial function $h(t)=−16t^2+275$ gives the height of a ball t seconds after it is dropped from a 275-foot tall bridge. Find the height after $t=2$ seconds.
The polynomial function $h(t)=−16t^2+90$ gives the height of a ball t seconds after it is dropped from a 175-foot tall bridge. Find the height after $t=1$ seconds.

Answer

The height is $156$ feet.
The height is $211$ feet.
The height is $74$ feet.

Graph of Polynomial

Find the polynomial that makes this graph.

$(x+1)(x-2)(x-3).png$

Answer

$(x+1)(x-2)(x-3)$

Find the polynomial that makes this graph.

$(x-1)(x+1)(x-2)(x-3).png$

Answer

$(x-1)(x+1)(x-2)(x-3)$

Find the polynomial that makes this graph.

$(x-1)(x+1)(x-2).png$

Answer

$(x-1)(x+1)(x-2)$

Find the polynomial that makes this graph.

$(x-1)(x+1).png$

Answer

$x-1)(x+1)$

Find the polynomial that makes this graph.

$(x-1)(x+2)(x-2)(x-3).png$

Answer

$(x-1)(x+2)(x-2)(x-3)$

End Behavior

Find end behavior of

$f(x)=-8x^7-4x+5$
$f(x)=6x^2+3x+2$
$f(x)=x^3-4x^2+5$
$f(x)=-9x^{12}-4x^4+5$
$f(x)=x^4-4x+5$

Answer

As $x\to\infty$, $f(x)\to -\infty$ and as $x\to-\infty$, $f(x)\to \infty$
As $x\to\infty$, $f(x)\to \infty$ and as $x\to-\infty$, $f(x)\to \infty$
As $x\to\infty$, $f(x)\to \infty$ and as $x\to-\infty$, $f(x)\to -\infty$
As $x\to\infty$, $f(x)\to -\infty$ and as $x\to-\infty$, $f(x)\to -\infty$
As $x\to\infty$, $f(x)\to \infty$ and as $x\to-\infty$, $f(x)\to \infty$

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