Question

Given the table below, determine if the data represents a linear or an exponential function and find a possible formula for the function.

Answer 1

Option B. y = 2x

Explanation:

The given table in the question is

x 0 1 2 3 4

f(x) 0 2 4 6 8

As we know if the function is exponential or in the form of
`f(x) = (a)^(x)` then for x = 0 value of this exponential function will be f(0) = 1 but as per table f(0) = 0, so the given function is not an exponential function.

Therefore the given function is a linear function.

Linear function is always in the form of y = mx + c

Now f(0) = m×0 + c = 0

c = 0

f(1) = m×1 = 2

m = 2

Now we replace the values of m and c in y = mx + c

The equation will be y = 2x.

Option B. y = 2x is the answer.

Answer 2

Option b is correct.

Linear function ;

y =2x

Explanation:

The formula y=f(x)=mx +c ......[1] is said to be a linear function. That means the graph of this function will be a straight line on the (x, y) plane, where m represents slope and b is the y-intercepts.

Consider any points from the table;

(1, 2) and (2, 4)

substitute these point in [1] we get;

for (1, 2)

⇒x = 1 and f(x) = 2 we have

2 = m + c

or

c = 2- m ......[1]

for (2, 4) we have;

4 = 2m + c .....[2]

Now, substitute equation [1] into [2] we get;

4 = 2m + 2 -m

Combine like terms;

4 = m + 2

Subtract 2 from both sides we get;

4 -2 = m +2 -2

Simplify:

2 = m or

m = 2

Substitute the value of m = 2 in [1] to solve for c;

c = 2 -2 = 0

c =0

⇒ y = 2x +0

y = 2x

therefore, the data in the table represents the Linear function and a possible formula for the linear function is; y = 2x