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Identify the graph of the absolute value function f with the given

characteristics.
f has a range of (-∞, 7), and a graph that is symmetric about
the line x = 3, and has a y-intercept of 4.

Identify the graph of the absolute value function f with the given characteristics-example-1
User Mkhanoyan
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1 Answer

4 votes

Explanation:

the bottom left graph is correct.

the range is the interval or set of all valid y-values. we see that the y-values have a maximum at y = 7, and go down on both sides in all eternity and therefore to -infinity.

the graph is symmetric (that means mirrored around) the imaginary vertical line at x = 3 (left and right sides of the graph look like mirrored images of each other).

the y-intercept (that means the y-value when x = 0) is at y = 4 on the y-axis.

many greetings to your teacher from me !

the range is actually (-infinity, 7].

the way your teacher wrote it (with ")"), it means that 7 is NOT included, and therefore (3, 7) is not a valid point of the function. in that case that point must be marked with an "empty" dot (a dark circle with white content).

but the graphic shows no such marking, therefore (3, 7) IS a valid point and the range must be

(-infinity, 7]

User Neige
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