Think of the equation of a linear function:
Recall y = mx + b for vertical shifts, we just add or subtract from 'b' and that will move the line up or down accordingly.. However, for horizontal shifts, we will need to add or subtract from 'x'. Note that the slope or 'm' stays the same for each type of shift.
Now that we know how the shifts occur, we might consider a different form of the equation for a linear function: y = a(x - h) + k here the 'a' is just our slope, 'k' is our original y intercept, and 'h' will represent the amount of horizontal shift.
So to get the desired transformations of a horizontal shift to the left of 8 and a vertical shift of down 3 from our original function y = x, we can make the following changes: y = (x + 8) - 3 Now you might be confused with how we got the 'x + 8'.. Let's consider values of 'h'. For positive values of h, the result will be a shift to the right and for negative values of h the result will be a shift to the left. So since we want a shift to the left we need to use a '-8' and when we substitute that into our new form, y = (x - h) + k you can see the sign change.
Now we can simplify of course and get the final equation: y = x + 5 or in function form f(x) = x + 5
Center: 0,0
vertex: 5,0
vertex2 (-5,0)
Answer:
Since you state that capitalization is important, then we can see that it is not possible to solve the equation for F.
If that's correct, then the only point of this was that we need to pay attention to symbols when dealing with equations or expressions
Step-by-step explanation:
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each of the sides of your equation
by the value of
on each of your sides
(you get this because we solve the particular equation we added above)
on each of your sides
because it equals to
because it brings us closer and closer to the answer of
by the number
on each of your sides
