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Cerrena [4.2K]
3 years ago
11

Does the table represent an exponential function? Explain.

Mathematics
1 answer:
Ede4ka [16]3 years ago
5 0

Answer:

No, because as the x-values are increasing by a constant amount, the y-values are not being multiplied by a constant amount.

Step-by-step explanation:

We have a set of ordered pairs of the form (x, y)

If a function is exponential then the ratio between the consecutive values of y, is always equal to a constant.

This means that:

\frac{y_2}{y_1}=\frac{y_3}{y_2}=\frac{y_4}{y_3}=by1y2=y2y3=y3y4=b

This is: y_2=by_1y2=by1

Now we have this set of points {(-1, -5), (0, -3), (1, -1), (2, 1)}

Observe that:

\begin{gathered}\frac{y_2}{y_1}=\frac{-3}{-5}=\frac{3}{5}\\\\\frac{y_3}{y_2}=\frac{-1}{-3}=\frac{1}{3}\\\\\frac{3}{5}\neq \frac{1}{3}\end{gathered}y1y2=−5−3=53y2y3=−3−1=3153=31

Then the values of y are not multiplied by a constant amount "b"

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Stella graphs the equation y=1/3x – 2
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we have

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<u>Statements</u>

<u>case A)</u> The graph is a straight line.

The statement is True

Because, this is a linear equation (see the attached figure)

<u>case B)</u> The line passes through the origin.

The statement is False

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Verify

Substitute the value of x and y in the equation

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the point (0,0) is not a solution

therefore

The line does not pass through the origin

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The statement is True

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Verify

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The statement is False

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<u>case E)</u> The y-intercept of the line is 2

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we know that

The y-intercept is the value of y when the value of x is equal to zero

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find the value of y

y=\frac{1}{3}*0-2=-2

the y-intercept is equal to -2


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