Pre-Algebra Examples

Graph f(x) = square root of e^xx
Step 1
Find the domain for so that a list of values can be picked to find a list of points, which will help graphing the radical.
Tap for more steps...
Step 1.1
Set the radicand in greater than or equal to to find where the expression is defined.
Step 1.2
Solve for .
Tap for more steps...
Step 1.2.1
If any individual factor on the left side of the equation is equal to , the entire expression will be equal to .
Step 1.2.2
Set equal to .
Step 1.2.3
Set equal to and solve for .
Tap for more steps...
Step 1.2.3.1
Set equal to .
Step 1.2.3.2
Solve for .
Tap for more steps...
Step 1.2.3.2.1
Take the natural logarithm of both sides of the equation to remove the variable from the exponent.
Step 1.2.3.2.2
The equation cannot be solved because is undefined.
Undefined
Step 1.2.3.2.3
There is no solution for
No solution
No solution
No solution
Step 1.2.4
The final solution is all the values that make true.
Step 1.2.5
The solution consists of all of the true intervals.
Step 1.3
The domain is all values of that make the expression defined.
Interval Notation:
Set-Builder Notation:
Interval Notation:
Set-Builder Notation:
Step 2
To find the radical expression end point, substitute the value , which is the least value in the domain, into .
Tap for more steps...
Step 2.1
Replace the variable with in the expression.
Step 2.2
Simplify the result.
Tap for more steps...
Step 2.2.1
Multiply by .
Step 2.2.2
Rewrite as .
Step 2.2.3
Pull terms out from under the radical, assuming positive real numbers.
Step 2.2.4
The final answer is .
Step 3
The radical expression end point is .
Step 4
Select a few values from the domain. It would be more useful to select the values so that they are next to the value of the radical expression end point.
Tap for more steps...
Step 4.1
Substitute the value into . In this case, the point is .
Tap for more steps...
Step 4.1.1
Replace the variable with in the expression.
Step 4.1.2
Simplify the result.
Tap for more steps...
Step 4.1.2.1
Multiply by .
Step 4.1.2.2
The final answer is .
Step 4.2
Substitute the value into . In this case, the point is .
Tap for more steps...
Step 4.2.1
Replace the variable with in the expression.
Step 4.2.2
Simplify the result.
Tap for more steps...
Step 4.2.2.1
Reorder and .
Step 4.2.2.2
Pull terms out from under the radical.
Step 4.2.2.3
The final answer is .
Step 4.3
The square root can be graphed using the points around the vertex
Step 5