The basic structure of a linear function is y=mx+b (or +c, depending on your schools curriculum)
We need to find the slope (m), and the y-intercept (b/c)
To find the slope you can pick two random points, say (2,2) and (0,1)
The formula for the slope is this: m= y1-y2 / x1-x2
So if we substitute the points in, we get 2-1 / 2-0 = 1/2
Knowing the slope, it can be substituted into to the equation: y=1/2x + b
Then, if you notice the second point- (0,1), it’s the y-intercept. The y coordinate there is 1.
To check if this is correct, a random coordinate set can be picked and substituted in to find b.
y= 1/2x + b
2 = 1/2 *2 + b
2 = 1 + b
2-1=b
1=b
Therefore, the final linear function is y = 1/2 x + 1
We are given the following function:
f(x) = 4/(x+2) - 2
We are asked to determine the inverse of this function. To do that we will first change the "f(x)" for "y":
Now we will switch "x" and "y", like this:
Now we will solve for "y", first by adding 2 to both sides:
Now we multiply both sides by "y+2":
Now we divide both sides by "x+2":
Now we subtract 2 to both sides:
Now we change "y" for the inverse of f(x), that is:
And thus we found the inverse. A similar procedure can be used for function 2.
let x = orginal price of the shorts
$21 = x(100%-20%) * 1.05
$21 = x(80%) * 1.05
$21 = 0.8x * 1.05
Subtract 1.05 from both sides
$19.95 = 0.8x
Divide 0.8 from both sides
$24.9375 = x
So the orginal price of the shorts are about $24.94
1 is thousands
6 is tens
2 is tenths
5 is hundreds
5x + 50 +x
= 5x*2( square ) + 50
