Question

Which graph represents the function f(x)=2⋅4x ?

Answer 1

Answer: Graph C is the correct graph of the given function.

Explanation:

Since, given function
`f(x)= 2.{4^x}`

And, if x=0 then y-intercept =
`2.4^0=2`

Therefore, graph must be passes through point (0,2).(y-intercept)

And, if y=0 then x=-2 therefore, x-intercept is (-2,0)

But first, second and forth graph do not having the above x and y-intercept

Therefore, first, second and forth graph can not be the graph of the above function.

Here, only graph third has the same x and y-intercepts.

Hence, Graph C is the correct graph of the given function.

Answer 2

A graph represents the exponential function
`f(x)=2\cdot 4^x` include the following: C. graph C.

In Mathematics and Geometry, an exponential function can be represented by using the following mathematical equation:

`f(x)=a(b)^x`

Where:

• a represents the initial value or y-intercept.
• x represents x-variable.
• b represents the rate of change, common ratio, decay rate, or growth factor.

The y-intercept of any graph represents the point where the graph of a function crosses the y-axis when x is 0. Therefore, the y-intercept of this exponential function is given by;

`f(x)=2\cdot 4^x\\\\f(0)=2\cdot 4^0`

f(0) = 2 ⇒ (0, 2)

When x is 1, the corresponding output value is as follows;

`f(x)=2\cdot 4^x\\\\f(1)=2\cdot 4^1`

f(1) = 8 ⇒ (1, 8)

In this context, we can logically deduce that this exponential function
`f(x)=2\cdot 4^x` must pass through (0, 2) and (1, 8) as correctly depicted by graph C only.