Which function is a translation of the parent absolute value function? f(x) = f(x) = f(x) = f(x) =

An absolute value function is a function that contains an algebraic expression within absolute value symbols. Recall that the absolute value of a number is its distance from 0 on the number line.

The absolute value parent function, written as f(x)=|x|, is defined as

f(x)={x      if  x>00      if   x=0−x   if  x<0

To graph an absolute value function, choose several values of x and find some ordered pairs.

Plot the points on a coordinate plane and connect them.

Observe that the graph is V-shaped.

(1) The vertex of the graph is (0,0).

(2) The axis of symmetry (x=0 or y-axis) is the line that divides the graph into two congruent halves.

(3) The domain is the set of all real numbers.

(4) The range is the set of all real numbers greater than or equal to 0. That is, y ≥0.

(5) The x-intercept and the y-intercept are both 0.

Vertical Shift

To translate the absolute value function f(x )=|x| vertically, you can use the function

g(x)=f(x)+k.

When k>0, the graph of g(x) translated k units up.

When k<0, the graph of g(x) translated k units down.

Horizontal Shift

To translate the absolute value function f(x)=|x| horizontally, you can use the function

g(x)=f(x−h).

When h>0, the graph of f(x) is translated h units to the right to get g(x).

When h<0, the graph of f(x) is translated h units to the left to get g(x ).

Stretch and Compression

The stretching or compressing of the absolute value function y=|x| is defined by the function y=a|x|  where a is a constant. The graph opens up if a>0 and opens down when a<0.

For absolute value equations multiplied by a constant (for example,y=a| x|),if 0<a<1, then the graph is compressed, and if a>1, it is stretched. Also, if a is negative, then the graph opens downward, instead of upwards as usual.

More generally, the form of the equation for an absolute value function is y=a|x−h|+k. Also:

• The vertex of the graph is (h,k).
• The domain of the graph is set of all real numbers and the range is y≥k when a>0.
• The domain of the graph is set of all real numbers and the range is y≤k when a<0.
• The axis of symmetry is x=h.
• It opens up if a>0 and opens down if a<0.
• The graph y=| x|  can be translated h units horizontally and k units vertically to get the graph of y=a|x−h|+k.
• The graph y=a|x|  is wider than the graph of y=|x| if |a|<1 and narrower if |a|>1.

Gauthmathier3641

Grade 10 · 2021-10-28

Answer

A parent function： y = |{x}|; vertically stretch a factor of 2
B parent function： y = |{x}|; shift 6 units to the left
C parent function： y = |{x}|;
D parent function： y = |{x}|; reflect across the y-axis,horizontally shrink a factor of 4

Explanation

A
Describe the transformation: parent function： y = |{x}|; vertically stretch a factor of 2
Answer: parent function： y = |{x}|; vertically stretch a factor of 2
B
Describe the transformation: parent function： y = |{x}|; shift 6 units to the left
Answer: parent function： y = |{x}|; shift 6 units to the left
C
Describe the transformation: parent function： y = |{x}|;
Answer: parent function： y = |{x}|;
D
Describe the transformation: parent function： y = |{x}|; reflect across the y-axis,horizontally shrink a factor of 4
Answer: parent function： y = |{x}|; reflect across the y-axis,horizontally shrink a factor of 4

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