Teresa graphs the following 33 equations: y=2xy=2x, y=x2+2y=x2+2, and y=2x2y=2x2. She says that the graph of y=2xy=2x will event
ually surpass both of the other graphs. Is Teresa correct? Why or why not?
1 answer:
The correct question is
<span>Teresa graphs the following 3 equations: y=2x, y=x2+2, and y=2x2. She says that the graph of y=2x will eventually surpass both of the other graphs. Is Teresa correct? Why or why not?
we have that
y=2x
y=x</span>²+2
y=2x²
using a graph tool
see the attached figure
<span>We can affirm the following
</span>the three graphs present the same domain-----> the interval (-∞,∞)
The range of the graph y=2x is the interval (-∞,∞)
The range of the graphs y=x²+2 and y=2x² is the interval [0,∞)
therefore
<span>Teresa is not correct because the graph of y = 2x will not surpass the other two graphs since in the interval of [0, infinite) the three graphs present the same range</span>
<span>Teresa graphs the following 3 equations: y=2x, y=x2+2, and y=2x2. She says that the graph of y=2x will eventually surpass both of the other graphs. Is Teresa correct? Why or why not?
we have that
y=2x
y=x</span>²+2
y=2x²
using a graph tool
see the attached figure
<span>We can affirm the following
</span>the three graphs present the same domain-----> the interval (-∞,∞)
The range of the graph y=2x is the interval (-∞,∞)
The range of the graphs y=x²+2 and y=2x² is the interval [0,∞)
therefore
<span>Teresa is not correct because the graph of y = 2x will not surpass the other two graphs since in the interval of [0, infinite) the three graphs present the same range</span>
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Answer:
There are many ways you can write this as an equation:
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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>