Question

A quadratic function and an exponential function are graphed below. Which graph most likely represents the quadratic function?


f(x) because an increasing exponential function will eventually exceed an increasing quadratic function

g(x) because an increasing quadratic function will eventually exceed an increasing exponential function

g(x) because an increasing exponential f

Answer 1

@jdoe0001

Answer 2

hmmm I'm inclined towards the flatter one
because an exponential function shoots up "y" values really fast
while the quadratic is constrained to its "2" exponent

or one can say for exampl, let's take x=8 so \(\large x=8\implies
\begin{array}{llll}
y=2^x\to 2^8\to 256
\\ \quad \\
y=x^2\to 8^2\to 64
\end{array}\)

Answer 3

hmm I may have mixed up the values there lemme rewrite that

Answer 4

hmmm actually.. no, is ok anyhow... so as you can see
the exponential shoots up "y" farther than the quadratic

actually notice this -> http://fooplot.com/#W3sidHlwZSI6MCwiZXEiOiJ4XjIiLCJjb2xvciI6IiNEOTE0MTQifSx7InR5cGUiOjAsImVxIjoiMl4oeC0yKS0wLjIiLCJjb2xvciI6IiMwOTEwREIifSx7InR5cGUiOjEwMDAsIndpbmRvdyI6WyItNS40OTk5OTk5OTk5OTk5OTgiLCI3LjUwMDAwMDAwMDAwMDAwMiIsIi0xLjc1OTk5OTk5OTk5OTk5OTgiLCI2LjI0MDAwMDAwMDAwMDAwMSJdfV0-

Answer 5

so one can say the quadratic is g(x), since the quadratic is narrower, but that's only as they're close to 0

Answer 6

So since the quadratic is g(x) would the answer be
g(x) because an increasing quadratic function will eventually exceed an increasing exponential function

g(x) because an increasing exponential function will always exceed an increasing quadratic function until their graphs intersect

Answer 7

if you grab the graph, drag up up up
and find where they intersect , which is at y=16 more or less

you'll see the exponential gets narrower

Answer 8

g(x) because an increasing exponential function \(\bf \text{will always exceed}\) an increasing quadratic function \(\bf \text{until their graphs intersect}\)

Answer 9

hmm actually that graph doesn't at y=16.. anyyow.. .lemme put another up so you can see it :)
http://fooplot.com/#W3sidHlwZSI6MCwiZXEiOiJ4XjIiLCJjb2xvciI6IiNEOTE0MTQifSx7InR5cGUiOjAsImVxIjoiMl54IiwiY29sb3IiOiIjMDkxMERCIn0seyJ0eXBlIjoxMDAwLCJ3aW5kb3ciOlsiLTUuODU5OTk5OTk5OTk5OTk4IiwiNy4xNDAwMDAwMDAwMDAwMDIiLCItMC4yNjAwMDAwMDAwMDAwMTc4IiwiNy43Mzk5OTk5OTk5OTk5ODUiXX1d

Answer 10

ok thanks so the answer is g(x) because an increasing exponential function will always exceed an increasing quadratic function until their graphs intersect

Answer 11

yes

when close to 0, the quadratic will be narrower
as they intersect further up, the exponential just takes off