Write a rule for g that represents the indicated transformations of the graph of f.
1 answer:
The rule of g(x) is g(x) = 2 + 4(x - 4) + 12
Step-by-step explanation:
Let us revise some transformation
- If the function f(x) translated horizontally to the right by h units, then its image is g(x) = f(x - h)
- 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
∵ f(x) = + 2x + 6
∵ The graph of f(x) is stretched vertically by a factor of 2
- That means the y-coordinate of each point on the graph is multiplied
by 2, then y = 2.f(x) as the 2nd rule above
∴ y = 2[ + 2x + 6]
∴ y = 2 + 4x + 12
∵ The graph of 2.f(x) is translated 4 units to the right
- That means substitute every x by (x - 4) as the 1st rule above
∴ g(x) = 2 + 4(x - 4) + 12
The rule of g(x) is g(x) = 2 + 4(x - 4) + 12
Learn more:
You can learn more about transformation in brainly.com/question/2451812
#LearnwithBrainly
You might be interested in
The standard form for a parabola is (x - h)2 = 4p (y - k), where the focus is (h, k + p) and the directrix is y = k - p. If the parabola is rotated so that its vertex is (h,k) and its axis of symmetry is parallel to the x-axis, it has an equation of (y - k)2 = 4p (x - h), where the focus is (h + p, k) and the directrix (d)
is x = h - p.
So directrix is: y = k - p and the focus is at:
(h, k+p)
Since our focus is: (1, 3) and directrix is: y = 1,
thus h = 1, k+p = 3, and k-p = 1
Therefore k = 3-p, 3-p-p = 1, k = 3-p = 3-1 = 2
3-2p = 1, -2p = -3+1, -2p = -2, p = 1
Now we plug p, k, & h into standard form:
(x - h)2 = 4p (y - k)
y = 1/4 (x-1)^2 + 2
is x = h - p.
So directrix is: y = k - p and the focus is at:
(h, k+p)
Since our focus is: (1, 3) and directrix is: y = 1,
thus h = 1, k+p = 3, and k-p = 1
Therefore k = 3-p, 3-p-p = 1, k = 3-p = 3-1 = 2
3-2p = 1, -2p = -3+1, -2p = -2, p = 1
Now we plug p, k, & h into standard form:
(x - h)2 = 4p (y - k)
y = 1/4 (x-1)^2 + 2