The graph of f (x) = x + 5 is a vertical translation 5 units
1 answer:
Answer:
A horizontal translation of 5 units to the left.
Step-by-step explanation:
Given the parent linear function:
To shift vertically n units, we can simply add n to our function. Hence:
So, a vertical shift of 5 units up implies that n=5. So:
As given.
However, to shift a linear function horizontally, we substitute our x for (x-n), where n is the horizontal shift. So:
Where n is the horizontal shift.
For example, if we shift our parent linear function 1 unit to the right, this means that n=1. Therefore, our new function will be:
Or:
We notice that this is also a vertical shift of 1 unit downwards.
Therefore, we want a number n such that -n=5.
So, n=-5.
Therefore, it we shift our function 5 units to the left, then n=-5.
Then, our function will be:
Hence, we can achieve f(x)=x+5 from f(x)=x using a horizontal translation by translating our function 5 units to the left.
You might be interested in
By first principles, the derivative is
Use the binomial theorem to expand the numerator:
where
The first term is eliminated, and the limit is
A power of in every term of the numerator cancels with
in the denominator:
Finally, each term containing approaches 0 as
, and the derivative is
Answer:
The correct option is option (c).
Step-by-step explanation:
Right angled triangle:
- One angle must be 90° and other two angles are acute angle.
- The hypotenuses is the longest side of the triangle and opposite right angle.
- It follows the Pythagorean Theorem.
Given that,
∠QRP= 90°, ∠RPQ= 30°, ∠PQR = 60°
we know that,
for sin P , the opposite is QR.
The hypotenuse is PQ.
Therefore,