20 POINTS!! Two exponential functions are shown in the table.

Which conclusion about f(x) and g(x) can be drawn from the table?

The functions f(x) and g(x) are reflections over the x-axis.

The functions f(x) and g(x) are reflections over the y-axis.

The function f(x) is a decreasing function, and g(x) is an increasing function.

The function f(x) has a greater initial value than g(x)

Question

10-04-2017
Mathematics

contestada

20 POINTS!! Two exponential functions are shown in the table.

Which conclusion about f(x) and g(x) can be drawn from the table?

The functions f(x) and g(x) are reflections over the x-axis.

The functions f(x) and g(x) are reflections over the y-axis.

The function f(x) is a decreasing function, and g(x) is an increasing function.

The function f(x) has a greater initial value than g(x)

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InesWalston InesWalston · Answer 1 · 2018-11-15T11:34:38+01:00

Answer-

The functions f(x) and g(x) are reflections over the y-axis.

Solution-

While reflecting any point with coordinates (x, y) over y-axis or x=0 line, the point shifts to (-x, y)

[tex](x,y)\rightarrow (-x,y)[/tex]

While reflecting any point with coordinates (x, y) over x-axis or y=0 line, the point shifts to (x, -y)

[tex](x,y)\rightarrow (x,-y)[/tex]

The given functions are,

[tex]f(x)=2^x,\ g(x)=(\frac{1}{2})^x[/tex]

Applying the formula for reflection of f(x) over y axis would be,

[tex]\Rightarrow y=2^{-x}[/tex]

[tex]\Rightarrow y={(2^{-1})}^{x}[/tex]

[tex]\Rightarrow y={(\frac{1}{2})}^{x}[/tex]

This is the equation for g(x)

Therefore, f(x) and g(x) are reflections over the y-axis.

DelcieRiveria DelcieRiveria · Answer 2 · 2019-04-08T11:34:19+02:00

Answer:

The correct option is 2.

Step-by-step explanation:

The given functions are

[tex]f(x)=2^x[/tex]

[tex]g(x)=(\frac{1}{2})^x[/tex]

It can be written as

[tex]g(x)=(2)^{-x}[/tex]

When a function is reflected about the y-axis then

[tex](x,y)\rightarrow (-x,y)[/tex]

Since f(-x)=g(x), therefore functions f(x) and g(x) are reflections over the y-axis. Option 1 is incorrect and option 2 is correct.

The general exponential function is

[tex]h(x)=ab^x[/tex]

Where, a is initial value and b is growth factor.

The function f(x) is increasing function because b=2>1.

The function g(x) is decreasing function because b=1/2<1.

Therefore option 3 is incorrect.

[tex]f(0)=2^0=1[/tex]

[tex]g(0)=(\frac{1}{2})^0=1[/tex]

The initial value of both functions is 1.

Therefore option 4 is incorrect.