Respuesta :

frika

You make such translations with graph of the function [tex]f(x)= x^2-3x:[/tex]

  • a translation 8 units up, then [tex]f_1(x)= x^2-3x+8;[/tex]
  • a translation 3 units right, then [tex]h(x)= (x-3)^2-3(x-3)+8.[/tex]

If for each value of x, g(x) is 125% of h(x), then you should multiply the function h(x) by coefficient 1.25, then

[tex]g(x)= 1.25((x-3)^2-3(x-3)+8),\\ \\g(x)=1.25(x-3)^2-3.75(x-3)+10.[/tex].

Answer: [tex]g(x)=1.25(x-3)^2-3.75(x-3)+10.[/tex]

Using translation concepts, it is found that the rule for g is given by:

[tex]g(x) = 1.25x^2 - 3.75x + 10[/tex]

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  • The rule for f is given by: [tex]f(x) = x^2 - 3x[/tex]
  • Shifting a function a units up is the same as adding a to the rule, thus, shifting f(x) 8 units up:

[tex]f(x) + 8 = x^2 - 3x + 8[/tex]

  • Shifting a function f(x) a units to the right is finding f(x - a), and thus, shifting the shifted function given by f(x) + 8, 3 units to the right to find the rule for h:

[tex]h(x) = f(x + 3) = (x + 3)^2 - 3(x + 3) + 8 = x^2 + 6x + 9 - 3x - 9 + 8 = x^2 - 3x + 8[/tex]

  • g(x) is 125% of h(x), thus:

[tex]g(x) = 1.25h(x)[/tex]

[tex]g(x) = 1.25(x^2 - 3x + 8)[/tex]

[tex]g(x) = 1.25x^2 - 3.75x + 10[/tex]

Which is the rule for g.

A similar problem is given at https://brainly.com/question/4521517

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