Answer to Question #236711 in Algebra for Lara

Question #236711
Let g(x) be the transformation of f(x)= x2. Write the rule for g(x) using the change described.

1. horizontal compression by a factor of 1/5 followed by a vertical shift down 7 units and reflection across y-axis. ______________

2. reflection across the x-axis followed by a vertical stretch by a factor of 3, a horizontal shift 6 units left, and a vertical shift 4 units down. _____________
1
Expert's answer
2021-09-16T05:15:02-0400

1)

Parent Function: f(x) = x\\^2

There are:

  • A horizontal compression by a factor of \frac{1}{5}
  • A vertical shift down 7 units
  • A reflection across y-axis, means that b is negative

The general form for the rule is: f(x) = a \times f([b(x-h]) + k

Therefore, b = -5 because of horizontal compression by a factor of \frac{1}{5} and reflection across y-axis

k= - 7

Replacing b and k in the general form of the rule f(x) = a f[ b(x − h)] + k where f(x) = x\\^2 , we find, f(x) = (-5(x))\\^2 - 7

= f(x) = (-5(x))\\^2 - 7


2)

Parent Function: f(x) = x\\^2

The general form for the rule is: f(x) = a \times f([b(x-h]) + k

There are:

Reflection across the x-axis, indicating that a is negative

Vertical stretch by a factor of 3, means that a= -3

A horizontal shift 6 units left, means that h=-6

 A vertical shift 4 units down, means that k= -4

Replacing a, k, and h in the general form of the rule f(x) = a f[ b(x − h)] + k where f(x) = x\\^2 , we find f(x) = -3((x + 6)\\^2) - 4

= -3((x + 6)\\^2) - 4





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