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liberstina [14]
3 years ago
6

Given f(x) and g(x) = f(x + k), use the graph to determine the value of k.

Mathematics
1 answer:
dedylja [7]3 years ago
3 0

g(x) is basically transformed f(x). First, let's focus on f(x) graph. Notice how the graph has slope of 1 and intersect y-axis at (0,0).

Which means that our equation for f(x) is:

\large{f(x) = x}

Now then we focus on g(x). g(x) is f(x+k). That means if f(x) = x then f(x+k) would mean substitute x = x+k in the equation.

\large{f(x + k) = x + k }\\  \large{g(x) = x + k}

Next, we want to find the value of k. In the slope-intercept form or y = mx+b where m = slope and b = y-intercept. Notice the g(x) graph and see that the graph intersects y-axis at (0,4). Therefore k = y-intercept = 4.

\large{g(x) = x + 4}

Answer

  • g(x) = x+4
  • Therefore the value of k is 4.
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