The equation of g(x) is g(x) = 6x + 11
Step-by-step explanation:
Let us revise some transformation
- 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
- If the function f(x) translated vertically up by k units, then its image is g(x) = f(x) + k
- If the function f(x) translated vertically down by k units, then its image is g(x) = f(x) - k
∵ f(x) = 2x + 5
∵ The graph of f(x) is stretched vertically by scale factor 3
- That means multiply f(x) by 3
∴ The equation of the new graph is 3(2x + 5)
∵ The new graph is translated 4 units down
- That means subtract 4 from 3(2x + 5)
∴ The equation of g(x) is g(x) = 3(2x + 5) - 4
- Simplify the equation of g(x)
∴ g(x) = 3(2x) + 3(5) - 4
∴ g(x) = 6x + 15 - 4
- Add the like terms in the right hand side
∴ g(x) = 6x + 11
The equation of g(x) is g(x) = 6x + 11
Learn more:
You can learn more about the translation in brainly.com/question/2451812
#LearnwithBrainly
