Question

Determine whether each table or rule represents a linear or an exponential function. Explain why or why not.

1. y = 4 * 5^x
2. y = 12 * x
3. y = -5 * 0.25^x
4. y = 7x + 3

Answer 1

if any expression is set up like this y=mx+b it is linear.
so 4 for sure and 3 is you switch it to the y=mx+b format

Answer 2

From the list, the linear functions are y=12x and y=7x+3. The exponentials functions are 4*5^x and -5*0.25^x.

Explanation:

Any linear function can be expressed as:

y=mx+b

Where b and m are constants (Real numbers) and x is the variable of the function.

For option 2, we have:

m=12 and b=0

For option 4, we have:

m=7 and b=3

The exponential functions are functions that can be written as:

y=a.b^x

Here a and b represent the coefficient and the base of the exponential, both reals numbers, and x is the variable of the function.

For option 1, we have:

a= 4 and b=5

For option 3, we have:

a=-5 and b=0.25