Respuesta :
Answer:
[tex]g(x) = 3(5)^x[/tex] ----- vertically stretched by 3
[tex]g(x) = \frac{1}{3}(5)^x[/tex] ----- vertically compressed by 1/3
[tex]g(x) = 5^{\frac{1}{3} x}[/tex] ----- horizontally stretched by 3
[tex]g(x) = 5^{3x}[/tex] ----- horizontally compressed by 3
Step-by-step explanation:
Given
[tex]f(x) = 5^x[/tex]
[tex]g(x) = 3(5)^x[/tex]
[tex]g(x) = 1/3(5)^x[/tex]
[tex]g(x) = 5^{\frac{1}{3} x}[/tex]
[tex]g(x) = 5^{3x[/tex]
Required
Match each expression of g(x) to the appropriate transformation
When a function is stretched vertically, the transformation rule is:
[tex](x,y) \to (x,ay)[/tex]
[tex]|a| >1[/tex]
[tex]g(x) = 3(5)^x[/tex] implies that:
[tex](x,f(x)) = (x,3f(x))[/tex]
[tex]3f(x) = 3(5)^x[/tex]
Hence:
[tex]g(x) = 3(5)^x[/tex] ----- vertically stretched by 3
When a function is compressed vertically, the transformation rule is:
[tex](x,y) \to (x,ay)[/tex]
[tex]|a| <1[/tex]
[tex]g(x) = 1/3(5)^x[/tex] implies that:
[tex](x,f(x)) = (x,\frac{1}{3}f(x))[/tex]
[tex]\frac{1}{3}f(x) = \frac{1}{3}(5)^x[/tex]
Hence:
[tex]g(x) = \frac{1}{3}(5)^x[/tex] ----- vertically compressed by 1/3
When a function is stretched horizontally, the transformation rule is:
[tex](x,y) \to (ax,y)[/tex]
[tex]|a| <1[/tex]
[tex]g(x) = 5^{\frac{1}{3} x}[/tex] implies that:
[tex](x,f(x)) = (\frac{1}{3}x,f(x))[/tex]
[tex]f(\frac{1}{3}x) = 5^{\frac{1}{3} x}[/tex]
Hence:
[tex]g(x) = 5^{\frac{1}{3} x}[/tex] ----- horizontally stretched by 3
When a function is horizontally vertically, the transformation rule is:
[tex](x,y) \to (ax,y)[/tex]
[tex]|a| >1[/tex]
[tex]g(x) = 5^{3x[/tex] implies that:
[tex](x,f(x)) = (3x,f(x))[/tex]
[tex]f(3x) = 5^{3 x}[/tex]
Hence:
[tex]g(x) = 5^{3x}[/tex] ----- horizontally compressed by 3
Answer:
Answer:
g(x) = 3(5)^x ----- vertically stretched by 3
g(x) = 1/3(5)^x ----- vertically compressed by 1/3
g(x) = 5^1/3x. ----- horizontally stretched by 3
g(x) = 5^3x ----- horizontally compressed by 3
Step-by-step explanation:
