Question

Functions and Slope! Very important, please help! (file attached)

Answer 1

f o g simply means to plug g into f for the x value

Thus F(x) = m1(g(x)) + b1
which is then
F(x) = m1(m2x + b2) + b1
Distribute the m1 and you get:
F(x) = m1*m2*x + m1*b2 +b1

The highest degree then would be 1 (x^1, the degree of which is 1), making it still a line

Answer 2

thank you! so how would i find the slope of that line?

Answer 3

\[\frac{ \Delta y }{ \Delta x }\] is the slope formual

Answer 4

\[\Delta = change\]

Answer 5

how would you do that with this equation
F(x) [aka y] = m1*m2*x + m1*b2 +b1

Answer 6

slope is the coefficient of change attached to the variable, in this case the coefficients attached to x are m1*m2

Answer 7

what about m1*b2

Answer 8

if someone could help me out please :)

Answer 9

think of it like this:

m1 is a number, as is m2, b1, and b2

lets make up a variable, say b3 and say that b3 = m1*b2
b3 will be a number, correct? in a line equation, numbers represent the y intercept. In this case, you have two, b3 and b2, or we can combine like terms and say that b4 = b3 + b2

If you want to get technical, you can also do the same thing for the new slope, and say m3 = m1*m2

With all this substition, your new function looks like this:
F(x) = m3x + b4

Answer 10

oh! thank you so much! you're a huge help :)

Answer 11

btw, i have a test on functions soon, so i'll be posting a few more questions this evening, if you could take a look at some of them, i'd really appreciate it :)