Math

QuestionGraph the function f(x)=x+5f(x)=x+5.

Studdy Solution

STEP 1

Assumptions1. The function to be graphed is f(x)=x+5f(x) = x +5 . We are graphing in a two-dimensional Cartesian coordinate system3. We are using standard graphing conventions, with x representing the horizontal axis and f(x) (or y) representing the vertical axis

STEP 2

To graph the function, we first need to understand what type of function it is. The given function f(x)=x+5f(x) = x +5 is a linear function, which means it will form a straight line when graphed.

STEP 3

The general form of a linear function is f(x)=mx+cf(x) = mx + c, where m is the slope of the line and c is the y-intercept. In our case, the function f(x)=x+5f(x) = x +5 has a slope of1 (since there is no number in front of x, it is understood to be1) and a y-intercept of5.

STEP 4

The slope of the line tells us how steep the line is. A slope of1 means that for every1 unit increase in x, f(x) (or y) increases by1 unit.

STEP 5

The y-intercept tells us where the line crosses the y-axis. In this case, the line crosses the y-axis at the point (0,5).

STEP 6

To start graphing, first plot the y-intercept. This is the point (0,5) on the graph.

STEP 7

From the y-intercept, use the slope to find another point on the line. Since the slope is1, we can go up1 unit and right1 unit from the y-intercept to find another point. This point is (1,6).

STEP 8

Plot this point (1,6) on the graph.

STEP 9

Repeat the process of using the slope to find more points on the line. For example, from the point (,6), we can go up unit and right unit to find the point (2,7).

STEP 10

Plot this point (2,7) on the graph.

STEP 11

Continue this process to find as many points as you need to clearly draw the line.

STEP 12

Once you have enough points, draw a straight line through them. This line represents the function f(x)=x+5f(x) = x +5.
The graph of the function f(x)=x+5f(x) = x +5 is a straight line with a slope of and a y-intercept of5.

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