Answer:
a) see the plots below
b) f(x) is exponential; g(x) is linear (see below for explanation)
c) the function values are never equal
Step-by-step explanation:
a) a graph of the two function values is attached
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b) Adjacent values of f(x) have a common ratio of 3, so f(x) is exponential (with a base of 3). Adjacent values of g(x) have a common difference of 2, so g(x) is linear (with a slope of 2).
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c) At x ≥ 1, the slope of f(x) is greater than the slope of g(x), and the value of f(x) is greater than the value of g(x), so the curves can never cross for x > 1. Similarly, for x ≤ 0, the slope of f(x) is less than the slope of g(x). Once again, f(0) is greater than g(0), so the curves can never cross.
In the region between x=0 and x=1, f(x) remains greater than g(x). The smallest difference is about 0.73, near x = 0.545, where the slopes of the two functions are equal.
Answer: 180 degrees clockwise
Step-by-step explanation:
Slope-intercept form:
y = mx + b
"m" is the slope, "b" is the y-intercept (the y value when x = 0 or (0,y))
For lines to be parallel, their slopes have to be the SAME.
The given line's slope is 5/3, so the parallel line's slope is also 5/3
y = 5/3x + b
To find "b", plug in the point (3,6) into the equation
y = 5/3x + b
6 = 5/3(3) + b
6 = 5 + b
1 = b
y = 5/3x + 1
Answer:
5
Step-by-step explanation:
First, find the equation of the line:
put it in the form y = mx + b where m is the slope and b is the y-intercept
You already have m = 2, so y = 2x + b.
Then, since you know (1, 3) is a solution so you can plug x = 1 and y = 3 into the equation to find out what b is.
3 = 2 * 1 + b
3 = 2 + b
1 = b
This means the equation of the line is y = 2x + 1.
Then, since you're trying to find out what y is when x = 2, you can plug in x = 2 into the equation:
y = 2 * 2 + 1
y = 4 + 1
y = 5
5 is the answer
Answer:
y=-5/3x-2
Step-by-step explanation:
