SOLUTION: (a) Graph the function f(x)= x^3 - 4 (b) Approximate to the nearest tenth, the real root of the equation f(x)= x^3

SOLUTION: (a) Graph the function f(x)= x^3 - 4 (b) Approximate to the nearest tenth, the real root of the equation f(x)= x^3 - 4 = 0 please help me

Question 92199This question is from textbook Algebra and Trigonometry
: (a) Graph the function f(x)= x^3 - 4
(b) Approximate to the nearest tenth, the real root of the equation
f(x)= x^3 - 4 = 0 please help me This question is from textbook Algebra and Trigonometry

Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
a) "Graph the function f(x)= x^3 - 4"

In order to graph , we need to plot some points.
We can start at any x value, so lets start at x=-2

Lets evaluate

Start with the given polynomial

Plug in

Raise -2 to the third power to get -8

Now combine like terms

So when ,

So our 1st point is (-2,-12)

----Now lets find another point----

Lets evaluate

Start with the given polynomial

Plug in

Raise -1 to the third power to get -1

Now combine like terms

So when ,

So our 2nd point is (-1,-5)

----Now lets find another point----

Lets evaluate

Start with the given polynomial

Plug in

Raise 0 to the third power to get 0

Remove any zero terms

So when ,

So our 3rd point is (0,-4)

----Now lets find another point----

Lets evaluate

Start with the given polynomial

Plug in

Raise 1 to the third power to get 1

Now combine like terms

So when ,

So our 4th point is (1,-3)

----Now lets find another point----

Lets evaluate

Start with the given polynomial

Plug in

Raise 2 to the third power to get 8

Now combine like terms

So when ,

So our 5th point is (2,4)

Now lets make a table of the values we have calculated

Now plot the points

Now connect the points to graph (note: the more points you plot, the easier it is to draw the graph)

b)
"approximate to the nearest tenth, the real root of the equation
f(x)= x^3 - 4 = 0 "

add 4 to both sides

Take the cube root of both sides

So the solution is approximately 1.5874010519682 which rounds to 1.6
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