Describe how to transform the graph of g(x)= ln x into the graph of f(x)= ln (3-x) -2.

A

Step-by-step explanation:

Note the following 3 points with respect to a function given as y = f(x).

1. The function y = f(-x) is a reflection across the y-axis

2. The function y = f(x+a) is a horizontal translation a units left and y = f(x-a) is a horizontal translation a units right

3. the function y = f(x) + a is a vertical translation a units up and y = f(x) - a is a vertical translation a units down

Dissecting the transformed function of  f(x) = ln (3-x) -2   w.r.t   f(x) = ln x, we see:

1. x is replaced with -x, so reflection across y-axis

2. we have a horizontal shift in left side because the argument of ln is (3-x) or (-x+3)

3. We have vertical shift 2 units down because there is a -2 after the functional part of ln(3-x)

Looking at the choices, A is the right answer.

answer. d.289 hope that

region b will make the inequalities y < 2x + 1 and y > -x - 2 true ⇒ answer a

step-by-step explanation:

* lets study the graph and the inequality to solve the question

- the inequality y > -x - 2

∵ the form of the inequality is y > mx + c , m is the slope of the line

  and c is the y-intercept (the line intersect y-axis at point (0 , c)

∴ c = -2 that means the line intersect the y-axis at point (0 , -2)

∵ the sign of the inequality is >

∴ we shad the part over the line

  region a and b

- the inequality y < 2x + 1

∵ the form of the inequality is y > mx + c , m is the slope of the line

  and c is the y-intercept (the line intersect y-axis at point (0 , c)

∴ c = 1 that means the line intersect the y-axis at point (0 , 1)

∵ the sign of the inequality is <

∴ we shad the part under the line

  region b and c

∵ the common region between the two lines is region b

∴ region b will make the inequalities y < 2x + 1 and y > -x - 2 true