Using translation concepts, it is found that the rule for g is:
[tex]g(x) = \frac{x^2}{5} - 8[/tex]
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- The parent function is: [tex]f(x) = x^2[/tex].
- Shrinking a function f(x) vertically by a factor of [tex]0 < a < 1[/tex] is equivalent to: [tex]a \times f(x)[/tex]
- f(x) by a factor of 1/5:
[tex]\frac{1}{5} \times f(x) = \frac{1}{5} \times x^2 = \frac{x^2}{5}[/tex]
- Shifting a function down a units is the same as finding [tex]f(x) - a[/tex].
- Down 8 units, then, the rule for g is:
[tex]g(x) = \frac{x^2}{5} - 8[/tex]
A similar problem is given at https://brainly.com/question/11000713
