F(x)=-1x-1
1) Pick 2 points on the line (i chose (-4,3) and (3,-4)
2) Find slope of the line using the 2 points. (work below)
3) Find y-intercept, which is the point where y-axis and the line cross (y-intercept is -1).
4) Place both slope and y-intercept into slope-intercept form, y=mx+b (m=slope and b=y-intercept.)
5) Change y to f(x) (meaning function of x).
Work:
3-(-4)/-4-3=3+4/-4-3=7/-7=-1
y-intercept equals -1 also.
y=mx+b
y=-1x+(-1)
y=-1x-1
f(x)=-1x-1<---Answer
To find the average speed in miles per hour, you will create a rate using the number of miles to the number of hours in 45 minutes.
54 miles in 0.75 hours (45 minutes)
To make this a unit rate or miles per hour, divide the number of miles by the time.
54/0.75 = 72 mph
The train traveled an average speed of 72 mph.
The period of a function is the length along the x-axis that is covered by one complete cycle of the function. Ours starts "up", so we need a period to cover up down up down (with the first "up" being our starting point). It looks like the whole up down up down thing happens within a span of
.The amplitude means how high does it go up the y-axis. Ours goes up to 2 and down to negative 2, so the amplitude is 2. For part b, the maximum values between 0 and pi/2 occur at 0 and pi/2, the minumum occur at pi/4 (there's only 1), and the zeros (where the graph goes through the x-axis) occur at pi/8 and 3pi/8.
First, we put the values of the given point into the general equation, giving:
0 = m * -1 + b .......(1)
Now plug in the given value of m into equation (1), giving:
0 = 2 + b ........(2)
Solving equation (2), we find that b = -2.
Now we can write the required equation as:
y = -2x - 2