Unit 55: Four Graph Problems

These are problems that, unsurprisingly, give you four graphs as answer choices and ask you to pick the correct one that represents a function. The purpose of the problems is to test your knowledge of how functions work and ability to graph them.  Once you know what to look for, these can be some of the easier problems.

What to look for on linear equation problems:

  • The y intercept (set x to 0)
  • The slope (you may have to first transform the equation into slope-intercept form)

Here’s a straightforward example.

Which of the following is the graph of the equation = 2− 5 in the xy-plane?


  1. Look for the y-intercept.
  2. Evaluate the slope.
  3. Draw your own graph if necessary.

Back to our example: We can look and see the slope is positive 2, so we can immediately rule out A) and B).  Next, we set x = 0 and see that the y intercept is -5.  This leads us very clearly to D).

You may also encounter this type of question in polynomial form.

If the function has four distinct zeros, which of the following could represent the complete graph of in the xy-plane? 

Remember from your earlier unit on polynomial zeros – this is the same as crossing or tangent to the x-axis.  Which graph shows this happening four times?  Only C).

Here’s a harder polynomial question:


The function is defined by the equation above. Which of the following is the graph of = −f (x) in the xy-plane? 

This is where we’ll utilize the third part of our strategy: drawing our own graph.

Plug in some x values to the equation at the top, and come up with the corresponding y values:

Now make all of the y values negative, to evaluate -f(x).


Now draw a graph with the values paired with the -f(x) values and see which answer choice looks the same.

Answer choice C) is correct.