Answer:
its Aor the first option because it has repeated x values making it not a function.
You can use the definition:

Then if

we have

Then the derivative is

I'm guessing the second part of the question asks you to find the tangent line to <em>f(x)</em> at the point <em>a</em> = 0. The slope of the tangent line to this point is

and when <em>a</em> = 0, we have <em>f(a)</em> = <em>f</em> (0) = -2, so the graph of <em>f(x)</em> passes through the point (0, -2).
Use the point-slope formula to get the equation of the tangent line:
<em>y</em> - (-2) = 3 (<em>x</em> - 0)
<em>y</em> + 2 = 3<em>x</em>
<em>y</em> = 3<em>x</em> - 2
Step 1
<u>Find the slope of the function f(x)</u>
we know that
The formula to calculate the slope between two points is equal to

Let

substitute



Step 2
<u>Find the y-intercept of the function f(x)</u>
The y-intercept is the value of the function when the value of x is equal to zero
in this problem the y-intercept of the function is the point 
so
the y-intercept is equal to 
Step 3
Verify each case
we know that
the equation of the line into slope-intercept form is equal to

where
m is the slope
b is the y-intercept
<u>case A) </u>
In this case we have

therefore
the function of case A) does not have the same slope as the function f(x)
<u>case B) </u>
In this case we have

therefore
the function of case B) does not have the same slope and y-intercept as the function f(x)
<u>case C) </u>
In this case we have

therefore
the function of case C) does have the same slope and y-intercept as the function f(x)
<u>case D) </u>
In this case we have

therefore
the function of case D) does not have the same y-intercept as the function f(x)
therefore
<u>the answer is</u>

Two equivalent fractions to represent the part of the migration a monarch butterfly can complete in 1 week is
or
.
<h3>What is a fraction?</h3>
A fraction is a mathematical expression that shows the relationship between parts vs total. In a fraction, the part is written first and it is known as the numerator. On the other hand, the total is written below and it is known as the denominator.
<h3>How to write a fraction?</h3>
Here are the steps to write a fraction:
- Find the total.
- Find the part.
- Write the fraction.
Based on this, in the chart, the part of the migration these butterflies can complete in a week are the squares in green, while the total is the total squares. This means the fraction for this situation is:
Moreover, you can simplify this fraction and find an equivalent one by dividing the denominator by the numerator as:
Note: This question is incomplete because there is a missing image; below I attach the missing section.
Learn more about fractions in: brainly.com/question/1301963