Sketch the graphs of the function by making a table of values.

Question

Answer 1

You want to put in some values for x and find results from the functions.

f(x) = √(x+4)

When x = 0, f(0) = √(0 + 4) = √4 = 2

When x = 1, f(1) = √(1 + 4) = √5 (slightly bigger than 2). These results can be hard to plot so make life easier by trying to determine values for x that produce easy to plot numbers.

For instance, values that would produce perfect squares in this case such as 4, 9, 16, 25, etc.

f(5) = √(5 + 4) = √9 = 3

f(12) = √(12 + 4) = √16 = 4

f(21) = √(21 + 4) = √25 = 5

So your table of values for f(x) = √(x + 4) might be

x f(x)

--------

0 2

5 3

12 4

21 5

for g(x) = |x| - x, we can see that any value of x>0 results in 0. g(1) = 0, g(2) = 0, g(50) = 0, etc.

g(0) = |0| - 0 = 0

g(1) = |1| - 1 = 0

g(2) = |2| - 2 = 0

But negative values give positive results.

g(-1) = |-1| - (-1) = 1 + 1 = 2

g(-2) = |-2| - (-2) = 2 + 2 = 4

g(-3) = |-3| - (-3) = 3 + 3 = 6

So a table of values for g(x) = |x| - x might be

x g(x)

---------

0 0

1 0

2 0

3 0

-1 2

-2 4

-3 6

From both of these tables it's easy to plot the values onto a graph.

Answer 2

1) f(x) =√ x+4 , you can take different values for x and calculate f(x), put the only restriction here is that the value of x+4 has to be always positive because we have square root, x≥ -4

you can take x= -4, f(x) =√ -4+4=0

x= -3, f(x) =√ -3+4 = 1

x=0 , f(x) =√ 0+4 = 2

x= 2, f(x) =√2+4 = √ 6

x=5, f(x) =√ 5+4= √ 9 = 3

using these points you can sketch the graph.

2) g(x) = ΙxΙ - x

you can take any values for x, let us start with negative values,

x= -5, g(x) = Ι-5Ι - (- 5) = 5+5 =10

x= -3 g(x) = Ι-3Ι - (- 3) = 3+3 =6

x= -1, g(x) = Ι-1Ι - (-1) = 1+1 = 2

so for all negative values g(x) is positive value , and the slope = 2

x=0 , g(x) =0

x=1 g(x) = Ι1Ι - 1 =1-1=0

x=2 g(x) = Ι2Ι - 2 =2 -2=0

you can see that for all positive values for x , g(x) will be zero.

using these points you can sketch the graph.