# The point (2, 4) is translated to which point when y = 2^x is translated to y = 2^(x+1) + 3 (4, 1), (1, 7), (7, 1), (1, 4)

embizze | High School Teacher | (Level 1) Educator Emeritus

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Given `f(x)=a(x-h)+k` we see the following transformations to the base function f(x):

a: a performs a vertical stretch or compression (dilation). Also, if a<0 the graph is reflected over the x-axis.

h: h performs a horizontal translation. Note that (x-2) moves the graph 2 units right while (x+2) moves the graph 2 units left.

k: k performs a vertical translation. (x-h)+2 moves the graph up 2, while (x-h)-2 moves the graph down 2.

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So, we are given `y=2^(x+1)+3` . Using `y=2^x` as the base function, every point on the base graph is moved 1 unit left and 3 units up. In particular, the point (2,4)-->(1,7)

justaguide | College Teacher | (Level 2) Distinguished Educator

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When `y = 2^x` , `2^2 = 4` which gives the point (2, 4). When this is translated to `y = 2^(x + 1) + 3` , for x = 1, y = `2^(1 +1) + 3` = `2^2 + 3` = 4 + 3 = 7

The point is translated to (1, 7).