Math

QuestionGraph the function f(x)=x+5f(x)=x+5. Identify the points A, B, C, and D on the graph.

Studdy Solution

STEP 1

Assumptions1. The function is f(x)=x+5f(x) = x +5 . We are asked to graph the function

STEP 2

The function f(x)=x+5f(x) = x +5 is a linear function, which means it will graph as a straight line. The slope of the line is the coefficient of xx, which is1, and the y-intercept is the constant term, which is5.

STEP 3

To graph the function, we first plot the y-intercept. The y-intercept is the point where the line crosses the y-axis. In this case, the y-intercept is5, so we plot the point (0,5).

STEP 4

Next, we use the slope to find another point on the line. The slope is the ratio of the change in y to the change in x, often described as "rise over run". In this case, the slope is1, which means for every1 unit we move to the right on the x-axis, we move up1 unit on the y-axis.

STEP 5

Starting from the y-intercept (0,5), we move1 unit to the right and1 unit up to get to the point (1,). We plot this point on the graph.

STEP 6

We can repeat the process to find more points if necessary, but since this is a linear function, two points are enough to define the line. We draw a straight line through the points (0,5) and (1,6).
The graph of the function f(x)=x+5f(x) = x +5 is a straight line with a slope of1 and a y-intercept of5.

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