Question

For the graph, which are possible functions ƒ, g, and h?
https://dlap.gradpoint.com/Resz/~0.gsyqJFIicnUyUA6.1ipNM0RXMrziFMZIUysm-pECjcn-637I1KzHD6DVYJI/7234256,D76/Assets/questions/quiz/precalculus/pcalexpo/IMG73449.png

Answer 1

@Vocaloid

Answer 2

notice how g is the "steepest", f is in the middle, and h is the least steep

so the rate of change for g should be the farthest away from 0, then f, then finally h should have the lowest rate of change

see what you can get from that

Answer 3

g=2, h=-2?

Answer 4

since these are exponential functions they should be written in the form

y = (starting value)(growth/decay factor)^x

Answer 5

I don't understand

Answer 6

remember it's asking for a function so you can't just say a number, it has to be a complete function in terms of x

Answer 7

to review: an exponential function is written in the form

y = ab^x
where a is the starting value, b is the growth or decay factor

Answer 8

for example, g(x) has the y-intercept (0,2) so (a) must be 2

it's decreasing so we can give it the decay value, 0.5 (that means it decreases by 50% each time)

so as an example, we can assign y = 2(0.5)^x to g

Answer 9

now, we know that f is less steep than h, so let's say it decays only 20% each time instead of 50%

so the function for f could be y = 2(0.8)^x
(since 100% - 20% = 80 percent)

Answer 10

so, using this logic, we know that all of them are in the form

y = 2(___)^x

and we know that h is the steepest, f is the middle, and h is the least steep

so you will see which set of functions out of your choices will produce three graphs, where h is the steepest, and l is the least steep, using the logic I have outlined

Answer 11

if you're still confused try graphing the equations they give you and you'll start to see the pattern

Answer 12

so, F(x)=1/8,g(x)=1/9,h(x)=1/7

Answer 13

\(\color{#0cbb34}{\text{Originally Posted by}}\) @Vocaloid
remember it's asking for a function so you can't just say a number, it has to be a complete function in terms of x
\(\color{#0cbb34}{\text{End of Quote}}\)

Answer 14

these are exponential functions, so once again, your f, g, and h must be in the form

___(___)^x