Question

graph f. start by plotting a few points and then sketch the graph of f.
f(x)=x+5
to sketch the graph of f, begin by plotting a few points.
plot (- 3,f(- 3)).
(0, 0)

Explanation:

Step1: Calculate f(-3)

Substitute \( x = -3 \) into \( f(x) = x + 5 \). So \( f(-3) = -3 + 5 = 2 \). Thus, the point is \( (-3, 2) \).

Step2: Calculate f(0)

Substitute \( x = 0 \) into \( f(x) = x + 5 \). So \( f(0) = 0 + 5 = 5 \). Thus, the point is \( (0, 5) \) (note: the original (0,0) is incorrect for this function).

Step3: Plot points and sketch

We can also find another point, say when \( x = 3 \), \( f(3) = 3 + 5 = 8 \), so the point is \( (3, 8) \). Now, plot the points \( (-3, 2) \), \( (0, 5) \), \( (3, 8) \) (and others if needed) and draw a straight line through them since \( f(x)=x + 5 \) is a linear function (in the form \( y=mx + b \) with slope \( m = 1 \) and y-intercept \( b = 5 \)).

Answer:

To graph \( f(x)=x + 5 \):

1. Calculate function values for chosen \( x \)-values:

• For \( x=-3 \), \( f(-3)=-3 + 5 = 2 \) (point: \( (-3, 2) \))
• For \( x = 0 \), \( f(0)=0 + 5 = 5 \) (point: \( (0, 5) \))
• For \( x = 3 \), \( f(3)=3 + 5 = 8 \) (point: \( (3, 8) \))

1. Plot these points on the coordinate plane.
2. Draw a straight line through the plotted points (since it is a linear function with slope \( 1 \) and y-intercept \( 5 \)).