Is -3.45 closer to -3 or -4 on a number line please i really need help
1 answer:
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Answer:
31. 1) Vertical shift up 4 units.
2) Horizontal shift right 1 unit.
3) Vertically stretched by a factor of 3.
32.
Step-by-step explanation:
Some transformations for a function f(x) are shown below:
- If , the function is shifted up "k" units.
- If , the function is shifted down "k" units.
- If , the function is shifted left "k" units.
- If , the function is shifted right "k" units.
- If , the function is reflected over the x-axis.
- If and
, the function is stretched vertically by a factor of "b".
31. Given the function and the function
, we can notice that the transformations from the graph of f(x) to the graph of g(x) are:
1)
2)
3) , being
Therefore, we can conclude that the transformations necessary to transform the graph of f(x) to the graph g(x) are:
1) Vertical shift up 4 units.
2) Horizontal shift right 1 unit.
3) Vertical stretch by a factor of 3.
32. Knowing the parent function:
And given the transformations:
1) Reflection over the x-axis.
2) Horizontal shift left 3 units.
3) Vertical shift up 7 units.
We can define that the function g(x) is:
Answer:
B) vertical stretch
Step-by-step explanation:
Given that the cost of manufacturing x refrigerators is given by the function .
Now it says that the cost doubles for the year 2011 owing to higher raw material prices. So that means cost function will change from f(x) to 2f(x).
Now we need to decide the type of transformation from f(x) to 2f(x).
Remember that when f(x) changes to a*f(x) where value of "a" is greater than 1 then it stretches the function vertically by factor of "a".
in 2f(x), we have a=2
So that means "B) vertical stretch" is the correct choice.