Question

Is f(x)=x(x+5) a linear function?

Answer 1

Answer: No, it is not a linear function. It is a Quadratic function.

Explanation:

Given the following function:

`f(x)=x(x+5)`

You need to apply Distributive property:

`f(x)=(x)(x)+(x)(5)`

`f(x)=x^2+5x`

You can observe that the highest exponent of the function is "2", therefore, it is not a Linear function, but a Quadratic function in the form:

`f(x) = ax^2 + bx + c`

Where a, b, and c are numbers (
`a\\eq 0`)

Answer 2

f (x) = (x+5) is linear

Explanation:

We are given the following function and we are to determine if it is a linear function or not:

`f ( x ) = ( x + 5 )`

For a function to be linear, it must be written in the standard form
`y=mx+c` and its graph gives a straight line.

Whereas, when an equation is squared, its graph becomes a curved one which is not linear.

Therefore, the given function f (x) = (x+5) is linear.