Match function with its graph

Question

(A). f(x)=x²

(B). f(x)=x³

(C). f(x)= square root of x

(D). f(x)= absolute value of x

Answer 1

The best way to start this problem, in my opinion, is to set up a "T-chart" with x values on the left, and corresponding f(x) values on the right. Let's do that.

Let's look at f(x) = x² first. Let's pick some test values of x. I am going to pick 0, 1, 2, and 3. Let's put that in to the x column below.

x | f(x)

0 |

1 |

2 |

3 |

Now we want to use the given function to evaluate the f(x) values. In this case, it is pretty simple: just square each x value and place it in the right f(x) spot. We get:

x | f(x)

0 | 0

1 | 1

2 | 4

3 | 9

Let's do the same for f(x) = x³. Set up the T-table and pick test values.

x | f(x)

0 |

1 |

2 |

3 |

To evaluate, simply cube each of the x values and place it in the right f(x) spot.

x | f(x)

0 | 0

1 | 1

2 | 8

3 | 27

Now let's look at the f(x) = square root of x, commonly written as f(x) = sqrt(x). We will follow the same procedure as above, but we should be careful what x values we pick; we want the x values to turn into nice whole number f(x) values. We should pick numbers that are perfect squares, so that when we take the square root, the corresponding value is a positive integer. Let's pick the first 3 perfect squares: 1, 4, and 9.

x | f(x)

1 |

4 |

9 |

When we take the square root of these, we get:

x | f(x)

1 | 1

4 | 2

9 | 3

Finally, we have f(x) = absolute value of x, commonly written as f(x) = abs(x). If we recall what absolute value does, we remember that an absolute value turns negative numbers to positive numbers (for example abs(-7) = 7) and keeps positive numbers as positive numbers (for example abs(7) = 7). We now see that it will be important to pick a few negative numbers to see what the graph will look like. Let's pick -2, -1, 0, 1, and 2 to be our x values.

x | f(x)

-2 |

-1 |

0 |

1 |

2 |

Let's fill in the f(x) by taking the absolute value:

x | f(x)

-2 | 2

-1 | 1

0 | 0

1 | 1

2 | 2

Now that we have these values, match the points that you found to each graph. For example, the graph for f(x) = x² will contain the points (0, 0), (1,1), (1,4), (1,9).

As you gain more experience you will notice patterns with the graph. For example, absolute value graphs have a sharp bump. Similarly, x³ rises more quickly than x² which rises more quickly than sqrt(x).

Hope this helps!

Answer 2

Try testing a few points on each graph to get an idea of its shape. For example, for graph A, when x=0 , f(x)=0 so you know the graph should be have a point at the origin. Then try when x=1, f(x)= 1. When x=2, f(x)=4. Plot these points (try both positive and negative inputs) until you can see a matching graph. Hope this helps!