Simplify... (10x-8) + (4x+5)
2 answers:
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Option A: It is vertically stretched
Option B: it is shifted down
Solution:
The exponential function undergoes two transformations to
.
<u>To determine how the graph changes:</u>
Consider the given exponential function .
Let y = f(x)
Vertically compressed or stretched:
A vertically compression (stretched) of a graph is compressing the graph toward x-axis.
• if k > 1 , then the graph y = k• f(x) , the graph will be vertically stretched by multiplying each y coordinate by k.
• if 0 < k < 1 if 0 < k < 1 , the graph is f(x) vertically shrunk (or compressed) by multiplying each of its y-coordinates by k.
• if k should be negative, the vertical stretch or shrink is followed by a reflection across the x-axis.
Here, k = 5
So the graph will be vertically stretched.
Also, Adding 3 to the graph will move the graph 3 units down so, the graph is shifted down.
So, The graph is shifted down.
Hence option A and option B is the correct answer.
a) You are told the function is quadratic, so you can write cost (c) in terms of speed (s) as
... c = k·s² + m·s + n
Filling in the given values gives three equations in k, m, and n.
Subtracting each equation from the one after gives
Subtracting the first of these equations from the second gives
Using the next previous equation, we can find m.
Then from the first equation
[tex]28=100\cdot 0.01+10\cdot (-1)+n\\\\n=37[tex]
There are a variety of other ways the equation can be found or the system of equations solved. Any way you do it, you should end with
... c = 0.01s² - s + 37
b) At 150 kph, the cost is predicted to be
... c = 0.01·150² -150 +37 = 112 . . . cents/km
c) The graph shows you need to maintain speed between 40 and 60 kph to keep cost at or below 13 cents/km.
d) The graph has a minimum at 12 cents per km. This model predicts it is not possible to spend only 10 cents per km.
Step-by-step explanation: