Question

***WILL MEDAL***
You have two exponential functions. One has the formula h(x) = -2 x + 8. The other function, g(x), has the graph shown below.
https://gordon.owschools.com/media/o_anageo_ccss_2014/8/alg1_9_20_34_exponential.gif
Which inequality below is true on the indicated interval?
A. g(x) ≥ h(x) on the interval -2 ≤ x ≤ -1
B. h(x) ≤ g(x) on the interval -1 ≤ x ≤ 0
C. g(x) ≥ h(x) on the interval 0 ≤ x ≤ 1
D. h(x) ≤ g(x) on the interval 1 ≤ x ≤ 2

Answer 1

@ChillOut @mathstudent55 @Jadeishere @Elsa213 @welshfella @paki @ParthKohli @uri

Answer 2

@TheSmartOne

Answer 3

Is h(x) \(2^{x}+8\)?

Answer 4

i think so

Answer 5

Because it'll be completely different if it's \(2^{x+8}\)

Answer 6

i think its the first one

Answer 7

All right... So let's find g(x)'s equation. Since we know it is an exponential function, it has the following form: \(a^{x}+z\). For the first and easiest part, we can find z by simply making x=0. This gives z=3, which is the "y intercept".

Answer 8

My guess is D...?

Answer 9

Are you guessing or did ou try to finish it? xD

Answer 10

All right, moving on... So to find a, we just make x=1, so we have g(1)=a+3, and since we have the value of g(1), which is 6, we can do the following: \(6=a^{1}+3,a=3\). So we have \(g(x)=3^{x}+3,\)

Answer 11

This is just confusing me...

Answer 12

I'm just finding the equation for g(x). Now I can keep moving on the problem

Answer 13

okay

Answer 14

Oh god, I've found an major error. But all right, I'll redo, with the same steps.

Answer 15

g(x)=\(a^{x}+z\)
g(0)=3, so 1+z= 3, z=2.
g(1)=6, so a + 2=6 and a=4

We have \(g(x)=4^{x}+2\)

Answer 16

Now we test the options... Just plug in the values in the fuctions and check if the statements are true or false! Can you do that?

Answer 17

yes! thank you.

Answer 18

No problem!

Answer 19

I'm still here if you get stuck.

Answer 20

im still getting D

Answer 21

All right, let me check, one moment.

Answer 22

It seems you're right.
g(1) = 6, f(1) = 6
g(2) = 18, f(2) = 4
So g(1)=f(1)
and g(2)>f(2).

Answer 23

Okay thank you

Answer 24

No problem. If you need help, just ask.

Answer 25

okay