Domain: all real numbers
range: y>6
range: y>6
Please help me with this
1 answer:
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Answer:
g(x) = 4 sin(x - 3)
Step-by-step explanation:
* Lets revise some transformation
- If the function f(x) translated horizontally to the right by h units, then
the new function g(x) = f(x - h)
- If the function f(x) translated horizontally to the left by h units, then
the new function g(x) = f(x + h)
- If the function f(x) translated vertically up by k units, then the new
function g(x) = f(x) + k
- If the function f(x) translated vertically down by k units, then the
new function g(x) = f(x) – k
- A vertical stretching is the stretching of the graph away from the
x-axis
- If k > 1, the graph of y = k • f(x) is the graph of f(x) vertically
stretched by multiplying each of its y-coordinates by k.
- A vertical compression is the squeezing of the graph toward
the x-axis.
- If 0 < k < 1 (a fraction), the graph of y = k • f(x) is the graph of f(x)
vertically compressed by multiplying each of its y-coordinates by k.
* Lets solve the problem
∵ f(x) = sin(x)
∵ f(x) is stretching vertically by a factor of 4
∴ f(x) multiplied by 4
∵ f(x) is shifting 3 units to the right
∴ We will change x to (x - 3)
∵ The new function is g(x)
∴ g(x) = 4 sin(x - 3)
- The attached graph for more understand
f(x) is the red graph
g(x) is the blue graph
