SOLUTION: I need help making the equations 10. A function f is given, and the indicated transformations are applied to its graph (in the given order). Write the equation for the final g

Question 1137308: I need help making the equations

10. A function f is given, and the indicated transformations are applied to its graph (in the given order). Write the equation for the final graph.

10a. f(x) = x^3; shift upward 3 units and shift 2 units to the right.

10b. f(x) = sqrtx; reflect in the y-axis, shrink vertically by a factor of 1/2, and shift upward 2 units.

10c. f(x) = |x|; shift to the left 1 unit, stretch vertically by a factor of 3, and shift upward 5 units.

Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
10a. f(x) = x^3; shift upward 3 units and shift 2 units to the right.

shift up 3 units becomes x^3 + 3
shift to the right 2 units becomes (x-2)^3 + 3

here's what happens.

when x is equal to 0, y = x^3 becomes y = 0^3 which becomes y = 0.
when x is equal to 0, y = x^3 + 3 becomes y = 0^3 + 3 which becomes y = 0 + 3 which becomes y = 3.
when x = 2, y = (x-2)^3 + 3 becomes y = 0^3 + 3 which becomes y = 0 + 3 which becomes y = 3.

here's the progression.

$$$

10b. f(x) = sqrtx; reflect in the y-axis, shrink vertically by a factor of 1/2, and shift upward 2 units.

here's what happens.

when x = 5, y = sqrt(x) becomes y = sqrt(5) which becomes y = 2.236 rounded to 3 decimal digits.
when x = -5, y = sqrt(-x) becomes y = sqrt(-(-5)) which becomes y = sqrt(5) which becomes y = 2.236 rounded to 3 decimal digits.
when x = -5, y = 1/2 * sqrt(-x) becomes y = 1/2 * sqrt(-(-5)) which becomes y = 1/2 * sqrt(5) which becomes y = 1/2 * 2.236 which becomes y = 1.118 rounded to 3 decimal digits.
when x = -5, y = 1/2 * sqrt(-x) + 2 becomes y = 1/2 * sqrt(-(-5)) + 2 which becomes y = 1/2 * sqrt(5) + 2 which becomes y = 1/2 * 2.236 + 2 which becomes y = 1.118 + 3 which becomes y = 3.118 rounded to 3 decimal digits.

here's the progression.

$$$

10c. f(x) = |x|; shift to the left 1 unit, stretch vertically by a factor of 3, and shift upward 5 units.

here's what happens.

when x = 1, y = abs(x) becomes y = abs(1) which becomes y = 1.
when x = 0, y = abs(x+1) becomes y = abs(1) which becomes y = 1.
when x = 0, y = 3 * abs(x+1) becomes y = 3 * abs(1) which becomes y = 3 * 1 which becomes y = 3.
when x = 0, y = 3 * abs(x+1) + 5 becomes y = 3 * abs(1) + 5 which becomes y = 3 * 1 + 5 which becomes y = 3 + 5 which becomes y = 8.

here's the progression.

$$$

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