Answer:
Part 1)
Part 2)
Part 3)
Step-by-step explanation:
we have
The parent function is
This is a vertical parabola open upward with vertex at origin (0,0)
Part 1) Reflection over the x-axis
The rule of the reflection across the x=axis is equal to
(x,y) ------> (x,-y)
so
f(x) -----> g(x)
The function g(x) will be
Part 2) Horizontal shift left 3 units
The rule of the translation is
(x,y) ------> (x-3,-y)
so
f(x) -----> g(x)
The function g(x) will be
Part 3) Vertical shift up 7 units
The rule of the translation is
(x,y) ------> (x,y+7)
so
f(x) -----> g(x)
The function g(x) will be
Answer:
10. Expanded vertically by 3, shifted left 2 and up 4.
11. Shifted right 6 and up 7.
Step-by-step explanation:
This sort of question involves matching patterns. You need to know what the various transformations look like, and what that means for a specific parent function.
Here are the transformations used in this problem:
- f(x -a) . . . . shift f(x) to the right by "a" units
- f(x) +a . . . . shift f(x) up by "a" units
- a·f(x) . . . . . vertically scale f(x) by a factor of "a"
For these problems, the parent function is f(x) = 1/x.
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10. The multiplier of 3 in the numerator (3/x) means the function has been scaled vertically (expanded) by a factor of 3.
The replacement of x with x+2 means the function has been shifted to the right by -2 units. That is the same as shifted left 2 units.
The addition of 4 to the function value means the function has been shifted up by 4 units.
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11. We note the numerator is still 1, so there is no vertical expansion. The replacement of x with x-6 means a right shift by 6 units. The addition of 7 to the function value means a shift up by 7 units.
Answer:
D
Step-by-step explanation:
When you simplify the expression you start by subtracting 5 from both sides. This gives you 0.2x > -3. Then to isolate "x" you divide both sides by 0.2. This gives you x > -15, which is shown in the number line.
I don’t understand the question can you explain a lil more
Answer:
55
Step-by-step explanation:
2x+5 x-5 combine these to get 3x
then you would divide 180 by 3
so u would get 60 = x
60-5 =55