Calculus 1 : Graphing Functions
Study concepts, example questions & explanations for Calculus 1
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Example Questions
Example Question #1 : How To Graph Functions Of Curves
A
B
C
D
For which of the graphs of 
A
B
D
C
A
The condition reads 'the limit of f of x as x approaches three from the left'. Note that we're not looking at x as it approached negative three. Only A and B have infinite limites at positive 3 (C and D show limits as x approaches negative 3), so the answer must be one of these. We can see that from the left, B approaches positive infinity at x=3 from the left, while A approaches negative infinity at x=3 from the left, so the correct answer is A.
Example Question #4 : How To Graph Functions Of Curves
On what interval is the following function decreasing?
Since this is a quadratic function with a positive first coefficient, we know it only has one local minimum and no other extrema. So all we have to do is find the x coordinate corresponding to this value and we will have one endpoint of our interval, and it will be decreasing constantly as you approach this point from the left.
Recall,
So, if we take the derivative of this quadratic, we get
So this is where our interval ends. Since there are no other local extrema, we know our interval is
Example Question #2 : Inflection Points
Which of the following is true about the twice-differentiable function 
Since the function 
Furthermore, there exists an inflection point at 
Thus at 
Therefore, the correct answer is 
Example Question #5 : How To Graph Functions Of Curves
Which one of the following could be the integral of 
Since the functions are added together, we can take each one seperately and add the results together.
The integral of 
The integral of 
which means it will equal
so combining these gives
as the integral, making 
Example Question #6 : How To Graph Functions Of Curves
Exponential Function
What is the graph of the folloiwng function:
None of the above
Use the following values to plot the graph:
Example Question #1 : How To Graph Functions Of Curves
Trigonometric Function
Graph the folloiwng function:
None of the above
Plot the graph for the following values:
Example Question #1 : How To Graph Functions Of Area
Graph of a piecewise-linear function 
Find
Find the area under the graph 
The areas are added to be:
Therefore,
Example Question #2 : How To Graph Functions Of Area
Find the area bounded by the curve 
The curve is in quadrant one over the given interval, which gives us the bounds of integration. Evaluating this definite integral yields the area we are after.
In order to performe the antiderivative, let 
so
Example Question #3 : How To Graph Functions Of Area
Find the area bounded by the curve 
The curve is positive over the given interval, so the endpoints of the interval will mark the bounds of integration. This function is very easy to integrate because the derivative of 
Example Question #2541 : Calculus
Find the area bounded by the curve 
This function is positve over the given interval, so the endpoints of the interval mark the bounds of integration. It is a straightforward integration that is solvable with u-substitution. Let 
so
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