# Graph g(x)=- square root of 3x+4

g(x)=-3x+4
Find the domain for y=-3x+4 so that a list of x values can be picked to find a list of points, which will help graphing the radical.
Set the radicand in 3x+4 greater than or equal to 0 to find where the expression is defined.
3x+4≥0
Solve for x.
Subtract 4 from both sides of the inequality.
3x≥-4
Divide each term by 3 and simplify.
Divide each term in 3x≥-4 by 3.
3×3≥-43
Cancel the common factor of 3.
Cancel the common factor.
3×3≥-43
Divide x by 1.
x≥-43
x≥-43
Move the negative in front of the fraction.
x≥-43
x≥-43
x≥-43
The domain is all values of x that make the expression defined.
Interval Notation:
[-43,∞)
Set-Builder Notation:
{x|x≥-43}
Interval Notation:
[-43,∞)
Set-Builder Notation:
{x|x≥-43}
To find the radical expression end point, substitute the x value -43, which is the least value in the domain, into f(x)=-3x+4.
Replace the variable x with -43 in the expression.
f(-43)=-3(-43)+4
Simplify the result.
Cancel the common factor of 3.
Move the leading negative in -43 into the numerator.
f(-43)=-3(-43)+4
Cancel the common factor.
f(-43)=-3(-43)+4
Rewrite the expression.
f(-43)=–4+4
f(-43)=–4+4
Simplify the expression.
Add -4 and 4.
f(-43)=-0
Rewrite 0 as 02.
f(-43)=-02
Pull terms out from under the radical, assuming positive real numbers.
f(-43)=-0
Multiply -1 by 0.
f(-43)=0
f(-43)=0
The final answer is 0.
0
0
0
The radical expression end point is (-43,0).
(-43,0)
Select a few x values from the domain. It would be more useful to select the values so that they are next to the x value of the radical expression end point.
Substitute the x value -1 into f(x)=-3x+4. In this case, the point is (-1,-1).
Replace the variable x with -1 in the expression.
f(-1)=-3(-1)+4
Simplify the result.
Multiply 3 by -1.
f(-1)=–3+4
Add -3 and 4.
f(-1)=-1
Any root of 1 is 1.
f(-1)=-1⋅1
Multiply -1 by 1.
f(-1)=-1
The final answer is -1.
y=-1
y=-1
y=-1
Substitute the x value 0 into f(x)=-3x+4. In this case, the point is (0,-2).
Replace the variable x with 0 in the expression.
f(0)=-3(0)+4
Simplify the result.
Multiply 3 by 0.
f(0)=-0+4
Add 0 and 4.
f(0)=-4
Rewrite 4 as 22.
f(0)=-22
Pull terms out from under the radical, assuming positive real numbers.
f(0)=-1⋅2
Multiply -1 by 2.
f(0)=-2
The final answer is -2.
y=-2
y=-2
y=-2
Substitute the x value 1 into f(x)=-3x+4. In this case, the point is (1,-7).
Replace the variable x with 1 in the expression.
f(1)=-3(1)+4
Simplify the result.
Multiply 3 by 1.
f(1)=-3+4
Add 3 and 4.
f(1)=-7
The final answer is -7.
y=-7
y=-7
y=-7
The square root can be graphed using the points around the vertex (-1.3‾,0),(-1,-1),(0,-2),(1,-2.65)
xy-1.3330-1-10-21-2.65
xy-1.3330-1-10-21-2.65
Graph g(x)=- square root of 3x+4

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