Answer: The answers are:
(1)
(2)
(3) (a)
Step-by-step explanation: The calculations are as follows:
(1) The given function is
We are to find the equation for the function g(x) is it represents f(x) after a horizontal translation of 2 units to the left.
When the function f(x) is translated 2 units to the left, the vertex of the function will shift from (0, 4) to (-2, 4).
So, the equation of g(x) will be
Thus, the equation for g(x) is
(2) The given function is
We are to find the value of
We have, after putting in the definition of f(x) that
Thus,
(3) We are to find the equation of a line in point-slope form for the following point and slope:
point: (1,−9) ; slope: 2.
We know that the equation of a line in point-slope form passing through the point (a, b) and slope m is given by
Therefore, the equation for the given line will be
Thus, the required equation of the line in point-slope form is
Option (a) is CORRECT.
Hence, all the questions are answered.