Write an equation for the line parallel to y = –2x – 5 that contains p(–8, 4).
1 answer:
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Answer:
y = 2|x| - 3
Step-by-step explanation:
We'll start with our parent function which is y = |x|. Notice that graph is translated down by 3 units. So, we'll add that:
Also notice that the ordered pair (1, -1) is on the graph. |1| = 1, so a translation of -3 should take it to -2 and it should have been (1, -2). But, it's not so it must be that the graph is stretched/compressed. If you multiply every point by 2, it gives us the result we want. Say for example, f(1) = 2|1| - 3 = 2 - 3 = -1. We get the point (1, -1) which is exactly what we want. We write compressions as (where a is the compression/stretching constant):
Our compression constant is 2, so our final answer is:
<em>y = 2|x| - 3</em>.
Answer:
No solution
Step-by-step explanation:
We have
For the sum it is not correct to assume
Note that for
it is assumed and in your case
for
In fact, considering a set we have
that satisfy
This means that, by definition
Therefore,
because the sum is empty.
For
we have other problems. Actually, this case is really bad.
Note that has no value. In fact, if we consider for the case
, the cosine function oscillates between
, and therefore it is undefined. Thus, we cannot evaluate
and then
has no solution
Answer:
The translation did not effect the domain
The translation effected the range
Step-by-step explanation:
The given graph represents f(x) = IxI
The domain of f(x) is {x : x ∈ R}, where R is the set of real numbers
The range of f(x) is {y : y ≥ 0}
The graph of g(x) is attached down
g(x) = IxI + 4
The domain of g(x) is {x : x ∈ R}, where R is the set of real numbers
The range of g(x) is {y : y ≥ 4}
The graph of g(x) is the image of the graph of f(x) after translate it 4 units up
∵ The translation is vertically
∴ The domain of f(x) = the domain of g(x)
∵ The domain of f(x) is {x : x ∈ R}
∴ The domain of g(x) is {x : x ∈ R}
∴ The translation did not effect the domain
∵ g(x) = f(x) + 4
∵ The range of f(x) is {y : y ≥ 0}
- Add 4 to the value 0
∴ The range of g(x) is {y : y ≥ 0 + 4}
∴ The range of g(x) is {y : y ≥ 4}
∴ The range of g(x) not equal the range of f(x)
∴ The translation effected the range
