The function f(x)=2x−5 is a linear function. Let g(x) represent f(x) after a horizontal translation 3 units to the right.
1 answer:
Answer:
the equation of g(x) is,
Step-by-step explanation:
The transformation of the function is defined as:
where, b represents the horizontal shift.
if b> 0 then, the function f(x) shifts b units left and if b< 0 ; then the function shifts b units right
As per the statement:
The function f(x)=2x−5 is a linear function.
It is given that:
g(x) represent f(x) after a horizontal translation 3 units to the right.
⇒
then
⇒
⇒
Therefore, the equation of g(x) is,
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9514 1404 393
Answer:
31.243 units
Step-by-step explanation:
The mnemonic SOH CAH TOA reminds you of the relationships between sides and angles in a right triangle. Using the attached figure, it is convenient to find the length of BE as an intermediate step in the solution.
Sin = Opposite/Hypotenuse
sin(30°) = BE/100
BE = 100·sin(30°)
Then ...
Tan = Opposite/Adjacent
tan(58°) = BE/x
x = BE/tan(58°) = 100·sin(30°)/tan(58°)
x ≈ 31.243 . . . . units
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<em>Comment on the figure</em>
The intermediate problem in creating the figure was to locate point D. That was accomplished by locating point C on a line at an angle of 58° CCW from the horizontal, using point B as a center. Then D is the intersection of BC with the x-axis. BE is drawn perpendicular to the x-axis.
