The function f(x)= 3^x was replaced with f(x)+k resulting in the function graphed to the right. What is the value of k?
To find the value of k, we need to examine the graph of the function f(x) = 3^x and compare it with the graph of the function f(x) + k.
Since the function f(x) = 3^x is an exponential function, its graph starts at the point (0, 1) and increases rapidly as x increases. The function f(x) = 3^x is always positive and continues to increase without bound.
When a constant k is added to the function f(x), it affects the vertical position of the graph. If k is positive, the graph will shift upward, and if k is negative, the graph will shift downward.
By looking at the graph provided, we can see that the graph starts at (0, 2) instead of (0, 1) and seems to follow the same exponential growth pattern as the function f(x) = 3^x. This indicates that k is equal to 1.
Therefore, the value of k is 1.
To determine the value of k, we need to analyze the transformation of the original function, f(x) = 3^x, to the new function f(x) + k.
Looking at the graph provided, we can observe that the graph of the new function is essentially the original function graph shifted vertically either up or down.
To find the amount of vertical shift, we need to determine the difference between the y-values of corresponding points on both graphs.
One common reference point is the y-intercept (where x = 0). For the original function, f(x) = 3^x, substituting x = 0 gives us f(0) = 3^0 = 1.
For the new function, f(x) + k, we can identify the corresponding y-coordinate by examining the graph, which appears to be f(0) + k = 2.
Since the resulting value is 2, we can conclude that k = 2 – 1 = 1.
Therefore, the value of k in the new function f(x) + k is 1.