Simplify
1 answer:
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Explanation: To graph the equation y = x - 2, the idea is simple.
We pick three values for <em>x</em>, plug them into the
equation, and find the corresponding values for <em>y</em>.
In order to do this in an organized way, we set up a chart.
Down the left side we make a column for our x's, down the right side we make a column for our y's, and in the middle we make a column for the side of the equation that contains the <em>x</em>, in this case, x - 2.
So reading the chart from left to right, we have our <em>x</em> or what we plug into the equation, then we have the x - 2 or what happens to the x when we plug it into the equation, and finally we have our <em>y</em> or what we end up with after plugging <em>x</em> into the equation.
So our first step in filling out the chart is choosing
the x's that we want to plug into the equation.
When graphing lines, I always choose three x's,
a positive number, zero, and a negative number.
The easiest numbers to pick are usually 1, 0, and -1.
So for 1, we plug a 1 into the equation for <em>x</em>
and we have y = (1) - 2 or -1
For 0 we plug a 0 into the equation for <em>x</em>
and we have y = (0) - 2 or -2.
For -1 we plug a -1 into the equation for <em>x</em>
and we have y = (-1) - 2 or -3.
So our points are (1, -1), (0, -2), and (-1, -3).
I looked at the x and y column to find those points.
Since our domain is all real numbers, we can connect these points based on the pattern that they are forming on the graph which is a line.
Answer:
The given statement that value 5 is an upper bound for the zeros of the function f(x) = x⁴ + x³ - 11x² - 9x + 18 will be true.
Step-by-step explanation:
Given
We know the rational zeros theorem such as:
if is a zero of the function
,
then .
As the is a polynomial of degree
, hence it can not have more than
real zeros.
Let us put certain values in the function,
,
,
,
,
,
,
,
,
From the above calculation results, we determined that zeros as
and
.
Hence, we can check that
Observe that,
,
increases rapidly, so there will be no zeros for
.
Therefore, the given statement that value 5 is an upper bound for the zeros of the function f(x) = x⁴ + x³ - 11x² - 9x + 18 will be true.