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A function is graphed on the coordinate plane.The function graphed has 3 branches. The first branch starts just above the x-axis and passes through the approximate points left parenthesis negative 5 comma .375 right parenthesis, left parenthesis negative 3 comma 1 right parenthesis, and left parenthesis negative 2 comma 2.4 right parenthesis, approaching but never reaching x equals negative 1. The second branch starts at the bottom of the graph just to the right of x equals negative 1 and passes through the approximate points left parenthesis 0 comma negative 4 right parenthesis, left parenthesis 0.5 comma negative 3.2 right parenthesis, left-parenthesis 1 comma negative 3 right-parenthesis, left parenthesis 1.5 comma negative 3.2 right parenthesis, and left parenthesis 2 comma negative 4 right parenthesis approaching but never reaching x equals 1. The third branch starts just to the right of x equals 3 and passes through the approximate points left parenthesis 4 comma 2.4 right parenthesis, left parenthesis 5 comma 1 right parenthesis, and left parenthesis 7 comma 0.375 right parenthesis approaching but never reaching the x-axis.
Question
Use the graph to answer the question.
Find the x- and y-intercepts of the function.
(1 point)
Responses

x-intercept: left parenthesis negative 4 comma 0 right parenthesis
y-intercept: none

x -intercept: Image with alt text: left parenthesis negative 4 comma 0 right parenthesis y -intercept: none

x-intercept: none
y-intercept: none

x -intercept: none y -intercept: none

x-intercept: none
y-intercept: left parenthesis 0 comma negative 4 right parenthesis

x -intercept: none y -intercept: Image with alt text: left parenthesis 0 comma negative 4 right parenthesis

x-intercepts: left parenthesis negative 9 comma 0 right parenthesis comma left parenthesis 9 comma 0 right parenthesis
y-intercept: left parenthesis 0 comma negative 4 right parenthesis

x -intercepts: Image with alt text: left parenthesis negative 9 comma 0 right parenthesis comma left parenthesis 9 comma 0 right parenthesis y -intercept: Image with alt text: left parenthesis 0 comma negative 4 right parenthesis
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1 answer

To find the x- and y-intercepts of the function described in the graph, we analyze the provided branches:

  1. X-intercept(s): The x-intercept occurs where the graph intersects the x-axis (y = 0). From your description, the first branch approaches but never reaches x = -1, and there is a point mentioned at (-4, 0). This indicates that the graph does indeed intersect the x-axis at (-4, 0). No other x-intercepts are provided as the other branches either do not reach the x-axis (as hinted by approaching descriptions) or continue in negative y-values. Therefore, the x-intercept is (-4, 0).

  2. Y-intercept: The y-intercept occurs where the graph intersects the y-axis (x = 0). From your description, there is a point at (0, -4), which indicates that the graph does intersect the y-axis at that point.

From this analysis, we can conclude:

  • X-intercept: (-4, 0)
  • Y-intercept: (0, -4)

Given these points, the correct response would be:

  • x-intercept: left parenthesis negative 4 comma 0 right parenthesis
  • y-intercept: left parenthesis 0 comma negative 4 right parenthesis