Absolute Value Functions & Transformations

Let's complete some examples together.

1

The function f(x) = | x | is graphed on the accompanying coordinate plane.

On the same axes, graph g(x) = | x | - 5 .

How does the graph of g(x) compare to the graph of f(x) ?

1

The function f(x) = | x | is graphed on the accompanying coordinate plane.

On the same axes, graph h(x) = -| 3x | .

How does the graph of h(x) compare to the graph of f(x) ?

1

The function f(x) = | x | is graphed on the accompanying coordinate plane.

On the same axes, graph k(x) = f(x - 6) .

How does the graph of k(x) compare to the graph of f(x) ?

Now, complete the rest of the problems for homework.

1

On the set of axes provided, graph the function
y = | x + 1 |

State the range of the function either in set or interval notation.

1

On the set of axes provided, graph the function
y = | x + 1 |

State the domain over which the function is increasing either in set or interval notation.

1

What is the minimum value of the function
y = | x + 3 | - 2 ?

1

On the set of axes provided, graph
f(x) = | x - 3 | + 2

1

Describe the effect that the transformation below has on the function
f(x) = | x | , where a > 0 .

g(x) = | x - a |

1

Describe the effect that the transformation below has on the function
f(x) = | x | , where a > 0 .

h(x) = | x | - a

1

On the set of axes provided, graph the function
y = | x - 3 |

Explain how the graph y = | x - 3 |
has changed from the related graph y = | x | .

1

On the set of axes provided, graph the function
f(x) = | 3x |

If g(x) = f(x) - 2 , how is the graph of f(x) translated to form the graph of g(x) ?

1

Absolute Value Functions & Transformations

Let's complete some examples together.

The function f(x) = | x | is graphed on the accompanying coordinate plane.

On the same axes, graph g(x) = | x | - 5 .

How does the graph of g(x) compare to the graph of f(x) ?

The function f(x) = | x | is graphed on the accompanying coordinate plane.

On the same axes, graph h(x) = -| 3x | .

How does the graph of h(x) compare to the graph of f(x) ?

The function f(x) = | x | is graphed on the accompanying coordinate plane.

On the same axes, graph k(x) = f(x - 6) .

How does the graph of k(x) compare to the graph of f(x) ?

Now, complete the rest of the problems for homework.

On the set of axes provided, graph the function
y = | x + 1 |

State the range of the function either in set or interval notation.

On the set of axes provided, graph the function
y = | x + 1 |

State the domain over which the function is increasing either in set or interval notation.

What is the minimum value of the function
y = | x + 3 | - 2 ?

On the set of axes provided, graph
f(x) = | x - 3 | + 2

Describe the effect that the transformation below has on the function
f(x) = | x | , where a > 0 .

g(x) = | x - a |

Describe the effect that the transformation below has on the function
f(x) = | x | , where a > 0 .

h(x) = | x | - a

On the set of axes provided, graph the function
y = | x - 3 |

Explain how the graph y = | x - 3 |
has changed from the related graph y = | x | .

On the set of axes provided, graph the function
f(x) = | 3x |

If g(x) = f(x) - 2 , how is the graph of f(x) translated to form the graph of g(x) ?

On the set of axes provided, graph the function
f(x) = | 3x |

If h(x) = f(x - 4) , how is the graph of f(x) translated to form the graph of h(x) ?

Let's complete some examples together.

The function f(x) = | x | is graphed on the accompanying coordinate plane.

On the same axes, graph g(x) = | x | - 5 .

How does the graph of g(x) compare to the graph of f(x) ?

The function f(x) = | x | is graphed on the accompanying coordinate plane.

On the same axes, graph h(x) = -| 3x | .

How does the graph of h(x) compare to the graph of f(x) ?

The function f(x) = | x | is graphed on the accompanying coordinate plane.

On the same axes, graph k(x) = f(x - 6) .

How does the graph of k(x) compare to the graph of f(x) ?

Now, complete the rest of the problems for homework.

On the set of axes provided, graph the function
y = | x + 1 |

State the range of the function either in set or interval notation.

On the set of axes provided, graph the function
y = | x + 1 |

State the domain over which the function is increasing either in set or interval notation.

What is the minimum value of the function
y = | x + 3 | - 2 ?

On the set of axes provided, graph
f(x) = | x - 3 | + 2

Describe the effect that the transformation below has on the function
f(x) = | x | , where a > 0 .

g(x) = | x - a |

Describe the effect that the transformation below has on the function
f(x) = | x | , where a > 0 .

h(x) = | x | - a

On the set of axes provided, graph the function
y = | x - 3 |

Explain how the graph y = | x - 3 |
has changed from the related graph y = | x | .

On the set of axes provided, graph the function
f(x) = | 3x |

If g(x) = f(x) - 2 , how is the graph of f(x) translated to form the graph of g(x) ?

On the set of axes provided, graph the function
f(x) = | 3x |

If h(x) = f(x - 4) , how is the graph of f(x) translated to form the graph of h(x) ?

Absolute Value Functions & Transformations

Absolute Value Functions & Transformations

Let's complete some examples together.

The function f(x) = | x | is graphed on the accompanying coordinate plane.On the same axes, graph g(x) = | x | - 5 .How does the graph of g(x) compare to the graph of f(x) ?

The function f(x) = | x | is graphed on the accompanying coordinate plane.On the same axes, graph h(x) = -| 3x | .How does the graph of h(x) compare to the graph of f(x) ?

The function f(x) = | x | is graphed on the accompanying coordinate plane.On the same axes, graph k(x) = f(x - 6) .How does the graph of k(x) compare to the graph of f(x) ?

Now, complete the rest of the problems for homework.

On the set of axes provided, graph the functiony = | x + 1 |State the range of the function either in set or interval notation.

On the set of axes provided, graph the functiony = | x + 1 |State the domain over which the function is increasing either in set or interval notation.

What is the minimum value of the functiony = | x + 3 | - 2 ?

On the set of axes provided, graphf(x) = | x - 3 | + 2

Describe the effect that the transformation below has on the functionf(x) = | x | , where a > 0 .g(x) = | x - a |

Describe the effect that the transformation below has on the functionf(x) = | x | , where a > 0 .h(x) = | x | - a

On the set of axes provided, graph the functiony = | x - 3 |Explain how the graph y = | x - 3 |has changed from the related graph y = | x | .

On the set of axes provided, graph the functionf(x) = | 3x |If g(x) = f(x) - 2 , how is the graph of f(x) translated to form the graph of g(x) ?

On the set of axes provided, graph the functionf(x) = | 3x |If h(x) = f(x - 4) , how is the graph of f(x) translated to form the graph of h(x) ?

Let's complete some examples together.

The function f(x) = | x | is graphed on the accompanying coordinate plane.On the same axes, graph g(x) = | x | - 5 .How does the graph of g(x) compare to the graph of f(x) ?

The function f(x) = | x | is graphed on the accompanying coordinate plane.On the same axes, graph h(x) = -| 3x | .How does the graph of h(x) compare to the graph of f(x) ?

The function f(x) = | x | is graphed on the accompanying coordinate plane.On the same axes, graph k(x) = f(x - 6) .How does the graph of k(x) compare to the graph of f(x) ?

Now, complete the rest of the problems for homework.

On the set of axes provided, graph the functiony = | x + 1 |State the range of the function either in set or interval notation.

On the set of axes provided, graph the functiony = | x + 1 |State the domain over which the function is increasing either in set or interval notation.

What is the minimum value of the functiony = | x + 3 | - 2 ?

On the set of axes provided, graphf(x) = | x - 3 | + 2

Describe the effect that the transformation below has on the functionf(x) = | x | , where a > 0 .g(x) = | x - a |

Describe the effect that the transformation below has on the functionf(x) = | x | , where a > 0 .h(x) = | x | - a

On the set of axes provided, graph the functiony = | x - 3 |Explain how the graph y = | x - 3 |has changed from the related graph y = | x | .

On the set of axes provided, graph the functionf(x) = | 3x |If g(x) = f(x) - 2 , how is the graph of f(x) translated to form the graph of g(x) ?

On the set of axes provided, graph the functionf(x) = | 3x |If h(x) = f(x - 4) , how is the graph of f(x) translated to form the graph of h(x) ?

The function f(x) = | x | is graphed on the accompanying coordinate plane.

On the same axes, graph g(x) = | x | - 5 .

How does the graph of g(x) compare to the graph of f(x) ?

The function f(x) = | x | is graphed on the accompanying coordinate plane.

On the same axes, graph h(x) = -| 3x | .

How does the graph of h(x) compare to the graph of f(x) ?

The function f(x) = | x | is graphed on the accompanying coordinate plane.

On the same axes, graph k(x) = f(x - 6) .

How does the graph of k(x) compare to the graph of f(x) ?

On the set of axes provided, graph the function
y = | x + 1 |

State the range of the function either in set or interval notation.

On the set of axes provided, graph the function
y = | x + 1 |

State the domain over which the function is increasing either in set or interval notation.

What is the minimum value of the function
y = | x + 3 | - 2 ?

On the set of axes provided, graph
f(x) = | x - 3 | + 2

Describe the effect that the transformation below has on the function
f(x) = | x | , where a > 0 .

g(x) = | x - a |

Describe the effect that the transformation below has on the function
f(x) = | x | , where a > 0 .

h(x) = | x | - a

On the set of axes provided, graph the function
y = | x - 3 |

Explain how the graph y = | x - 3 |
has changed from the related graph y = | x | .

On the set of axes provided, graph the function
f(x) = | 3x |

If g(x) = f(x) - 2 , how is the graph of f(x) translated to form the graph of g(x) ?

On the set of axes provided, graph the function
f(x) = | 3x |

If h(x) = f(x - 4) , how is the graph of f(x) translated to form the graph of h(x) ?

The function f(x) = | x | is graphed on the accompanying coordinate plane.

On the same axes, graph g(x) = | x | - 5 .

How does the graph of g(x) compare to the graph of f(x) ?

The function f(x) = | x | is graphed on the accompanying coordinate plane.

On the same axes, graph h(x) = -| 3x | .

How does the graph of h(x) compare to the graph of f(x) ?

The function f(x) = | x | is graphed on the accompanying coordinate plane.

On the same axes, graph k(x) = f(x - 6) .

How does the graph of k(x) compare to the graph of f(x) ?

On the set of axes provided, graph the function
y = | x + 1 |

State the range of the function either in set or interval notation.

On the set of axes provided, graph the function
y = | x + 1 |

State the domain over which the function is increasing either in set or interval notation.

What is the minimum value of the function
y = | x + 3 | - 2 ?

On the set of axes provided, graph
f(x) = | x - 3 | + 2

Describe the effect that the transformation below has on the function
f(x) = | x | , where a > 0 .

g(x) = | x - a |

Describe the effect that the transformation below has on the function
f(x) = | x | , where a > 0 .

h(x) = | x | - a

On the set of axes provided, graph the function
y = | x - 3 |

Explain how the graph y = | x - 3 |
has changed from the related graph y = | x | .

On the set of axes provided, graph the function
f(x) = | 3x |

If g(x) = f(x) - 2 , how is the graph of f(x) translated to form the graph of g(x) ?

On the set of axes provided, graph the function
f(x) = | 3x |

If h(x) = f(x - 4) , how is the graph of f(x) translated to form the graph of h(x) ?