Which of the following is the parent function of all absolute value functions?

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Sean W.

Algebra

8 months, 3 weeks ago

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Identify the parent function of f(x) =(x +3)3. Select the correct answer below: Constant Linear Quadratic Cubic Square Root Absolute Value

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So let's say I wanted to identify the parent function. What exactly is the parent function? Well, if I got rid of all the miscellaneous stuff, like anything inside or outside the function like this, plus three, the exponent will stay with, but there's nothing else outside. It would just be X. The third power. Okay, so what kind of function is this? Well, this is something raised to the third power, right? Anything raised the second power? That's quadratic x rays. The first is linear. Okay, absolute value of X is just the absolute function. What else do I have here in constant? Or the square root function would have? The square root constant would just be a number, see like a fixed number 123 or four. So it's none of these. So this is actually raised the third power. So this is what we call a cubic function would be my parent function.

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.

What is the parent function of all absolute value functions?

Which of the following is the parent function of all absolute value functions quizlet?

Which of the following are characteristics of the absolute value parent function?