Question

What's the difference between linear and exponential functions? @poojah can you help?

Answer 1

Hello!

Answer 2

Hi @Decarr432

Answer 3

Exponential means a function whose value is a constant raised to the power of the argument

Answer 4

Linear functions are those whose graph is a straight line

Answer 5

so this function \(x^x \) is not exponential

Answer 6

So what is x^x? is it linear?

Answer 7

no it is not linear

Answer 8

Exponential function is in the form of:
\(\color{#000000}{\displaystyle y=a(b)^x}\)

And the linear function is in the form of:
\(\color{#000000}{\displaystyle y=mx+b}\) (m could be 0, too)

Ok, but still, what is the difference?
Let me give you a hint for this.s s

The table for: \(\color{#000000}{\displaystyle y=a(b)^x}\)

\(\color{#000000}{\displaystyle x}\) \(\color{#000000}{\displaystyle y}\)

\(\color{#000000}{\displaystyle 1}\) \(\color{#000000}{\displaystyle a\cdot b }\)
\(\color{#000000}{\displaystyle 2}\) \(\color{#000000}{\displaystyle a\cdot b^2 }\)
\(\color{#000000}{\displaystyle 3}\) \(\color{#000000}{\displaystyle a\cdot b^3 }\)
\(\color{#000000}{\displaystyle 4}\) \(\color{#000000}{\displaystyle a\cdot b^4 }\)
(So wouldn't I multiply times b every time x goes up by 1?)



The table for: \(\color{#000000}{\displaystyle y=mx+b}\)

\(\color{#000000}{\displaystyle x}\) \(\color{#000000}{\displaystyle y}\)

\(\color{#000000}{\displaystyle 1}\) \(\color{#000000}{\displaystyle m+b }\)
\(\color{#000000}{\displaystyle 2}\) \(\color{#000000}{\displaystyle 2m+b }\)
\(\color{#000000}{\displaystyle 3}\) \(\color{#000000}{\displaystyle 3m+b }\)
\(\color{#000000}{\displaystyle 4}\) \(\color{#000000}{\displaystyle 4m+b }\)

(So wouldn't I add an "m" every time x goes up by 1?)