Question

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

Answer 1

f(x) = x + 4 x g(x)
-1 8
1 0
2 -4
@DanJS here it is

Answer 2

k

Answer 3

the y intercept is the point (x,y) = (0,y) when x is zero it will cross the Y axis, can you picture that

Answer 4

um nope

Answer 5

oh i see

Answer 6

When x axis line is at zero, you are in the y-axis

Answer 7

so what can you think about f(x) for it's y-intercept, what would you do ?

Answer 8

so y is 4 right?..

Answer 9

right, you set X=0, then you get the y-intercept F(x) = 0 + 4

Answer 10

so put dot on 4?

Answer 11

yes you can place a point at ( x , y) = (0 , 4)

Answer 12

similarly, if you want to graph a line, you need 2 points right?

so find now the X-intercept by doing the same thing, this time set Y=0 and figure X

Answer 13

are you talking about g(x)?than it would be 1...?

Answer 14

f(x) = y = x + 4

0 = x + 4

when y is zero, x is -4

second point (x , y) = ( -4 , 0)

Answer 15

oh i see

Answer 16

no still f(x), similar question, now you can graph the line, you have 2 points, the X and the Y intercepts

Answer 17

why would the 4 be negative? for o,-4

Answer 18

fixed sorry

Answer 19

ohok

Answer 20

FOr g(x), it looks like it is also a line, constant slope

Answer 21

so the other 4 would be negative?i thought it would be positive

Answer 22

wasnt the point 4,0?

Answer 23

No, when y = f(x) = 0 , you get
0 = x + 4
0 - 4 = x + 4 - 4

x = -4

the x intercept is -4

Answer 24

plus the slope is +1, the line must be climbing

Answer 25

ohok i get it and what were you saying about g(x)?

Answer 26

if you calculate the slope between points 1-2 and 2-3 or any 2 of those points, the slope is the same, it is a line of the form y = m*x+ b

Answer 27

a line has the same slope everywhere

Answer 28

yep, now you hav e

y = mx + b
y = -4*x + b

pick any point and put in (x,y) and solve b

Answer 29

b is the y intercept for that form of a line equation, y = (slope)*x + (y int)

Answer 30

see when x = 0, you get y=b, the y intercept

Answer 31

so what can be determined about both of their y intercepts

Answer 32

since you figured the slope is -4 for g(x)

y = -4*x+ b

use any point on g, i pick (x , y ) = (1 , 0) ... put into equation

0 = -4*(1) + b

what is b - (y intercept) for g?

Answer 33

-4

Answer 34

b = 4


thjey both have the same y-intercepts

Answer 35

0 = -4 + b

add 4 both side

b = 4

Answer 36

ok they all have same y intercepts?

Answer 37

yes, if you don't get something let me know

Answer 38

i get it so my answer would be they all have same y intercept. thanks and you know how you helped me with f(g((x) problem i am trying to do mine but cant get the answer. f(x) = 2x + 1 and g(x) = −5x + 2, solve for f(g(x)) when x = 3. dont you start with g(x) first?

Answer 39

i did -5 times 3 + 2

Answer 40

nvm i got it its -25

Answer 41

yeah, remember to figure the inner function first, then use that value to move outwards

Answer 42

yup i remember and id you have g(f((x) do you start with f first?

Answer 43

yep.

W[f(G(x))] G then f then W, keeping track of the values to use for each as you work outwards

Answer 44

what is w

Answer 45

i just added a third function, same idea, work middle to outside

Answer 46

ohoki am just learning about 2 function right now in algebra 2 lol but thxs

Answer 47

no prob