Answer:
f(x) reflect over the x-axis, vertically stretch by a factor 3, and
shift down 1 unit ⇒ 2nd answer
Explanation:
* To solve this problem you must to know some fact about
transformation
- If the function f(x) translated horizontally to the left
by h units, then the new function g(x) = f(x + h)
- If the function f(x) translated vertically up
by k units, then the new function g(x) = f(x) + k
- If the function f(x) translated vertically down
by k units, then the new function g(x) = f(x) – k
- A vertical stretching is the stretching of the graph away from
the x-axis
• if k > 1, the graph of y = k•f (x) is the graph of f (x) vertically
stretched by multiplying each of its y-coordinates by k.
- A vertical compression is the squeezing of the graph toward
the x-axis.
• if 0 < k < 1 (a fraction), the graph is f (x) vertically compressed
by multiplying each of its y-coordinates by k.
• if k should be negative, the vertical stretch or compress is
followed by a reflection across the x-axis.
* Now lets solve the problem
- From the graph
∵ The line passes through the points (0 , -1) and (-1 , 2)
∴ The slope of the line = (2 - -1)/(-1 - 0) = 3/-1 = -3
∵ The graph intersect the y-axis at point (0 , -1)
∵ The equation of any line ⇒ y = mx + c , where m is the slope
of the line and c is the y-intercept
∵ m = -3 and y-intercept = -1
∴ y = -3x - 1 ⇒ g(x) = -3x - 1
∵ f(x) = x
* From all the transformation above
# -3x means the graph reflected over the x-axis, vertically stretch
by a factor 3
# -1 means shift down 1 unit
# g(x) = -3f(x) - 1
∴ f(x) reflect over the x-axis, vertically stretch by a factor 3, and
shift down 1 unit
* The second answer