The leading coefficient of the function
will determine whether the graph opens up or down. If your leading coefficient is positive, the graph will open up and your vertex will be a minimum point. If a>0 (positive), the graph will open up.
Can an absolute value function be upside down?
Graphing the Absolute Value Function
We can translate, stretch, shrink, and reflect the graph. …
The graph of f (x) = – a| x – h| + k is an upside-down “V”
with vertex (h, k), slope m = – a for x > h and slope m = a for x < h. If a > 0, then the lowest y-value for y = a| x – h| + k is y = k.
Is an absolute value function increasing or decreasing?
The function is
increasing on [0,∞) and decreasing on (−∞,0]
. The relative minimum value of f is the same as the absolute minimum, namely 0 which occurs at (0,0). … There is also no absolute maximum value of f, since the y values on the graph extend infinitely upwards.
How do you know if absolute value is positive or negative?
- The absolute value of a positive number is the same number.
- The absolute value of a negative number makes it a positive number.
- Placing absolute value bars around 0 doesn’t change its value, so |0| = 0.
What is the turning point of an absolute value function?
The turning point being where
the absolute value changes between being positive and being negative
. This means we can change this absolute value equation into two simple equations, one that is true when x > 1 and the other true when x < 1. We then solve each one separately.
What kind of graph looks like an upside down V?
Whenever we have to Graph
Absolute value
, we have to consider positive values and negative values for x. The general shape will look like a ‘v’ (or in some cases, an upside down ‘v’ as we will see later).
Can an absolute minimum be a hole?
— *. _. *
holes and too can not be considered as absolute
extrema. (absolute) minimum and an (absolute) maximum on that interval.
What is the range of an absolute value function?
Since we have absolute signs, we must get only positive values by applying any positive and negative values for x in the given function. So, the range of absolute of absolute value is [0,∞).
How do you know if an absolute value has no solution?
Recall that an absolute value expression can never be less than zero. That is, a fully reduced absolute value expression must be greater than or equal to zero. If you’ve
simplified an absolute value equation and the value on the other side of the
equals sign is a negative number, the equation has no solution.
What happens if absolute value equal zero?
No matter if the number is to the left (negative) or right (positive) of zero on the number line,
the DISTANCE it is away from zero is going to be positive
. Hence, the absolute value is always positive (or zero if you are taking the absolute value of 0).
What happens when an absolute value equals zero?
In the case of only one solution, you end up with an absolute value expression equal to zero. Since this means that
the distance from zero on the number line is zero
, you end up with only one equation.
How do you describe an absolute value graph?
To graph an absolute value function,
choose several values of x and find some ordered pairs
. … (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.
What is the range for the parent function of absolute value?
Absolute values can never be negative, so the parent function has a range of [0, ∞).
