Is 20 a prime or composite number.
2 answers:
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We have been given a graph of function g(x) which is a transformation of the function
Now we have to find the equation of g(x)
Usually transformation involves shifting or stretching so we can use the graph to identify the transformation.
First you should check the graph of
You will notice that it is always above x-axis (equation is x=0). Because x-axis acts as horizontal asymptote.
Now the given graph has asymptote at x=-2
which is just 2 unit down from the original asymptote x=0
so that means we need shift f(x), 2 unit down hence we get:
but that will disturb the y-intercept (0,1)
if we multiply by 3 again then the y-intercept will remain (0,1)
Hence final equation for g(x) will be:
Answer/Step-by-step explanation:
a. Using a point on the graph, (6, 12), and the slope of the line, we can first generate an equation in the point-slope form, given as , where,
m = slope, and (a, b) is a point on the line.
Using two points, (6, 12) and (3, 21), let's find slope, m.
Using a point (6, 12) and slope, m = -3, generate an equation in the point-slope form by substituting a = 6, b = 12, and m = -3 in .
✅Equation in point-slope form would be:
Rewrite this to make it be in the slope-intercept form, .
Add 12 to both sides
✅The equation in slope-intercept form is
b. ✍️Based on the linear model, , the 30 represents b = y-intercept.
✅Therefore, it took Peter 30 mins long initially to deliver his package.
✍️Based on the linear model, , "-3" represents the slope.
✅Therefore, Peter's delivery time decreased 3 mins per day.