Question

I WILL MEDAL AND FAN
Below are two different functions, f(x) and g(x). What can be determined about their y-intercepts?

Answer 1

I see f(x). where is g(x) ?

Answer 2

x

g(x)


4

9


6

13


8

17

Answer 3

answer:

The function g(x) has a higher y-intercept.

The function f(x) has a higher y-intercept.

They both have the same y-intercept.

The relationship between y-intercepts cannot be determined.

Answer 4

the y-intercept is the "y value" where the line crosses the y-axis.
the y-axis is the up/down (vertical) axis

do you know the y-intercept for f(x) (from the graph) ?

Answer 5

thats all it gave me.
x is 4 6 8
g(x) is 9 13 17 @phi

Answer 6

yes. but first, where does the line in the graph cross the y-axis? Any idea ?

Answer 7

-1 ? @phi

Answer 8

yes. now we need to figure out what g(x) is doing

Answer 9

decreasing by 4

Answer 10

if we look for a pattern in g(x):
x 4 to 6 (x goes up by 2)
g(x) 9 to 13 (g(x) or "y" goes up by 4)

if we look at
x 6 to 8 (up by 2)
y 13 to 17 (up by 4)

so it looks like every time x goes up by 2, y goes up by 4
in terms of "slope" change in y: 4 divided by "change in x" 2 we get 4/2 = 2

Answer 11

if we go backwards, from x=4 to 2, y goes down by 4 from 9 to 5
then x=2 to 0 (down by 2) , y goes down from 5 to 1 (down by 4)
so at x=0, y is 1 (that is the y-intercept!)

Answer 12

of course, we could use equations

using two points , for example (4,9) and (6, 13)
we find the slope: (13-9) / (6-4) = 4/2 = 2
then we write

y = m x + b
replace m with the slope :

y= 2x + b
finally, "put in" one of the points (does not matter which one), so let's use (4,9)
9 = 2*4 + b
9 = 8 + b

now "solve for b" by adding -8 to both sides
9-8 = 8-8 + b
or
1 = b
that is the y-intercept

Answer 13

we can now answer the question
y-intercept of f(x) is -1
y-intercept of g(x) is +1

Answer 14

so the answer would be The function g(x) has a higher y-intercept. @phi

Answer 15

yes. "higher" means "bigger number" and 1 is bigger (above ) -1 on the y-axis.