Question

(02.05 LC) Given f(x) and g(x) = f(x + k), use the graph to determine the value of k. (1 point) Two lines labeled f of x and g of x. Line f of x passes through points 0, 4 and negative 4, 0. Line g of x passes through points negative 9, 0 and negative 4, 5. −4 −5 4 5

Answer 1

To find the value of k in the function g(x) = f(x + k), the horizontal shift between corresponding points on f(x) and g(x) is observed. The point (-4, 0) on f(x) shifted 5 units left to (-9, 0) on g(x), indicating that k equals -5.

Step-by-step explanation:

The question asks us to determine the value of k where g(x) is defined as f(x + k). We are given two functions f(x) and g(x) with their respective points on their graphs. The line f(x) passes through the points (0, 4) and (-4, 0), while the line g(x) passes through (-9, 0) and (-4, 5). To find k, we compare the shift along the x-axis from a known point on f(x) to its corresponding point on g(x).

Observing the graph, we can see that the point (-4, 0) on f(x) aligns with the point (-9, 0) on g(x). The horizontal shift from -4 to -9 is 5 units to the left, which indicates that k = -5. Therefore, the function g(x) is the function f(x) shifted to the left by 5 units, leading us to conclude that k = -5.