Home / Assignment Help / Which is the graph of the step function f(x)? f(x) = {-1×1 Image for option 1

Which is the graph of the step function f(x)? f(x) = {-1×1 Image for option 1

Answer:

Option B-  Yes; the domain values are at regular intervals and the range values have a common factor 4.

Step-by-step explanation:

Given : The data

(x) -5,   -4,  -3,   -2

(y) 0.5,  2,   8,   32

To find : The data shows an exponential function or not

Solution :

The general form of an exponential form is y=ab^x

To check whether the data give the exponential function we form equation with the help of two points and verify the other two points .

y=ab^x

Let x= -5 and y=0.5

0.5=ab^{-5}

frac{0.5}{b^{-5}}=a ……[1]

Let x= -4 and y=2

2=ab^{-4}

frac{2}{b^{-4}}=a ………[2]

Equate LHS because RHS is equal in equation [1] and [2]

frac{2}{b^{-4}}=frac{0.5}{b^{-5}}

frac{b^{-4}}{b^{-5}}=frac{2}{0.5}

b=4

Put back in [2]

frac{2}{4^{-4}}=a .

a=2times4^4

a=2times256=512

a=512 and b=4

Exponential function – y=4(512)^x

To verify this function put

1) x=-3

y=512(4)^{-3}

y=farc{512}{64}

y=8

The point satisfied.

2) x=-2

y=512(4)^{-2}

y=farc{512}{16}

y=32

The point satisfied.

Therefore, The given data is an exponential function y=4(512)^x

The domain values are at regular intervals and the range values have a common factor 4 because b=4 and the change happen but value of b remain same.

Hence, Option B is correct.

Yes; the domain values are at regular intervals and the range values have a common factor 4.

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