Question

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

Graph of two lines. f of x equals 1 over 3 x plus 2 and g of x equals 1 over 3 x plus 5.
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Answer 1

k = 3

Explanation:

From observation of the given graph, we can see that the lines of the two functions are parallel. This means that they have the same slope.

If we look at the y-intercepts of both lines, we can see that the y-intercept of function g(x) is 5 and the y-intercept of function f(x) is 2. Therefore, function g(x) is function f(x) shifted 3 units up. This is a vertical translation of 3 units up.

When translating a function up "a" units, add "a" to the function. Therefore, if g(x) is f(x) translated 3 units up, then g(x) = f(x) + 3. This means that k = 3.

Answer 2

Answer: 3

Reason:

To go from the blue line f(x) to the red line g(x), we shift up 3 units.

This means g(x) = f(x)+3.