Step-by-step explanation:
so, if I understand this correctly, the original function (shown in the graph) is
f(x) = sqrt(x)
the following transformations were done going from f(x) to h(x) :
x -> x + 4 as variable term moved the whole curve 4 units to the left. because now a specific functional value is calculated for a smaller x (by 4 units) than for the original f(x). e. g. let's call g(x) = sqrt(x + 4). then g(-4) = f(0). as mentioned, everything moved over to the left by 4 units.
sqrt(x) -> 3×sqrt(x) increased the range of the function (the generated y values) by the factor 3. was the functional result for a x value = 1, then it is now 3 for the same x value.
sqrt(x) -> sqrt(x) - 1 moved the whole curve down by 1 unit.
in summary, the whole original curve was moved 4 units to the left, then stretched upwards by the factor 3, and then that result was moved down by 1 unit.
so, e.g.
h(-4) = 3×f(0) - 1 = -1 point (-4, -1) corresponds to old (0, 0)
h(-3) = 3×f(1) - 1 = 2 point (-3, 2) corresponds to old (1, 1)
h(0) = 3×f(4) - 1 = 5 point (0, 5) corresponds to old (4, 2)
