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What is the equation of the function shown in the graph, given the equation of the parent function is f(x)=0.75x ?
A.) g(x) = 0.75^x + 3
B.) g(x) = 0.75^x + 2
C.) g(x) = 0.75^x - 1
D.) g(x) = 0.75^x - 2

What is the equation of the function shown in the graph given the equation of the parent function is fx075x A gx 075x 3 B gx 075x 2 C gx 075x 1 D gx 075x 2 class=

Respuesta :

f(x) = 0.75^x will pass through the point (0,1)  because  0.75^0  = 1

This graph passes through (0,3) so it has been translated up 2 units.

The answer is  b g(a) = 0.75^x + 2

Answer: The correct option is B.

Explanation:

The given parent function is,

[tex]f(x)=0.75^x[/tex]

Put x=0

[tex]f(0)=0.75^(0)[/tex]

[tex]f(0)=1[/tex]

It means the graph of parent function intersect the y-axis at 1.

From the given figure it is notices that the graph of function intersect the the y-axis at 3. It means the graph of parent function is shifted two units in upward direction.

If we add any constant k in the function, then the graph of function shifts upward by  k units and if we subtract any constant k from the function, then the graph of function shifts downward by  k units.

Since the graph shifted upward by 2 units so we have to add 2 in the parent function.

[tex]g(x)=f(x)+2[/tex]

[tex]g(x)=0.75^x+2[/tex]

Therefore, the correct option is B.

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