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What is the effect on the graph of [tex]$f(x)=x^2[tex]$[/tex] when it is transformed to [tex]$[/tex]h(x)=5x^2 + 10$[/tex]?

A. The graph of [tex]$f(x)$[/tex] is horizontally stretched by a factor of 5 and shifted 10 units up.

B. The graph of [tex]$f(x)$[/tex] is vertically stretched by a factor of 5 and shifted 10 units up.

C. The graph of [tex]$f(x)$[/tex] is vertically stretched by a factor of 5 and shifted 10 units to the left.

D. The graph of [tex]$f(x)$[/tex] is horizontally compressed by a factor of 5 and shifted 10 units to the left.



Answer :

Answer:

B. The graph of f(x) is vertically stretched by a factor of 5 and shifted 10 units up.

Step-by-step explanation:

  • in this case, h(x) has a  coefficient of 5 in front of the x² term, which means it’s vertically stretched by a factor of five compared to f(x)
  • The constant term 10 in h(x) represents a vertical shift and since it’s positive the graph of h is shifted upward by 10 units compared to the graph of f
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