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notsponge [240]
3 years ago
9

The graph of g(x) is a transformation of the graph of f(x)=3^x .

Mathematics
1 answer:
marshall27 [118]3 years ago
4 0

f(x)=3^x\\\\g(x)=3^{x+a}+b\\\\\text{We have the points (-2, 2) and (-1, 4). Substitute:}\\\\\underline{+\left\{\begin{array}{ccc}2=3^{-2+a}+b\\4=3^{-1+a}+b\end{array}\right}\qquad\text{subtract both sides of the equations}\\.\ \ -2=3^{-2+a}-3^{-1+a}\\-2=3^{-2}\cdot3^a-3^{-1}\cdot3^a\\-2=\dfrac{1}{3^2}\cdot3^a-\dfrac{1}{3}\cdot3^a\\-2=\left(\dfrac{1}{9}-\dfrac{1}{3}\right)\cdot3^a\\-2=\left(\dfrac{1}{9}-\dfrac{3}{9}\right)\cdot3^a\\-2=-\dfrac{2}{9}\cdot3^a\qquad\text{multiply both sides by}\ -\dfrac{9}{2}

3=3^a\\3^a=3^2\to a=2\\\\\text{substitute value of a to the second equation}\\\\3^{-1+2}+b=4\\3^1+b=4\\3+b=4\qquad\text{subtract 3 from both sides}\\b=1\\\\Answer:\ \boxed{g(x)=3^{x+2}+1}

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Mark is taking pledges for bike-a-thon fundraiser. John pledged $2.00, plus $1.75 for each mile Mark bikes. Kiara pledged $5.25,
Shkiper50 [21]

Answer:

The equation for the amount of dollars pledged in total is f(M) = 2.00M + 7.25, and the amount for just Kiara is f(M) = 0.25M + 5.25

Step-by-step explanation:

The amount they pledge up front is a constant and therefore need to be added to the end of the equation. The amount per mile should be a variable amount. This gets multiplied by the M variable. So we start with the Kiara amount.

0.25 per mile = 0.25M

5.25 pledged = 5.25

Now put them together to get f(M) = 0.25M + 5.25

Do the same with Mark.

1.75 per mile = 1.75M

2.00 pledged = 2.00

Now put them together to get f(M) = 1.75M + 2.00

To get the final total, we add both equations together.

f(M) =  0.25M + 5.25 + 1.75M + 2.00

f(M) = 2.00M + 7.25

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What is the perimeter of the triangle shown on the coordinate plane, to the nearest tenth of a unit?
Karo-lina-s [1.5K]

Let us find the co ordinates of each vertex of the triangle .

Vertex A ( in firs second quadrant) = ( -5 ,3)

vertex B in third quadrant = ( -5, -5)

vertex C in fourth quadrant = ( 4, -2)

let us use distance formula AB^2 = ( -5 - 3)^2 + (-5 - -5 )^2 = 64 + 0

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