Respuesta :
Answer:
This is the graph of a {\text{nonlinear function}}nonlinear functionstart text, n, o, n, l, i, n, e, a, r, space, f, u, n, c, t, i, o, n, end text.
The yyy-intercept of the graph is the function value y={{-6}}y=−6y, equals, minus, 6.
The xxx-intercepts of the graph are located at x={2}x=2x, equals, 2 and x={6}x=6x, equals, 6.
The greatest value of yyy is y={2}y=2y, equals, 2, and it occurs when x={4}x=4x, equals, 4.
For xxx between x=2x=2x, equals, 2 and x=6x=6x, equals, 6, the function value {y \, {\geq } 0}y≥0y, is greater than or equal to, 0.
Step-by-step explanation:
1 / 7
Let's use the graph to complete the sentences one by one.
Hint #22 / 7
A function with a constant rate of change produces a graph that is a line, and we say the function is linear. If the rate of change of the function is not constant, the graph will not be a line, and we say the function is nonlinear.
The graph shown is not a line. Therefore, we are looking at the graph of a nonlinear function.
Hint #33 / 7
The yyy-intercept of a graph is the value of the function when \red{x=0}x=0start color #df0030, x, equals, 0, end color #df0030. The yyy-intercept of this graph is the function value \blue{y=-6}y=−6start color #6495ed, y, equals, minus, 6, end color #6495ed.
Hint #44 / 7
The xxx-intercepts of a graph are the values of \red{x}xstart color #df0030, x, end color #df0030 for which \blue{y=0}y=0start color #6495ed, y, equals, 0, end color #6495ed. The xxx-intercepts of this graph are located at \red{x=2}x=2start color #df0030, x, equals, 2, end color #df0030 and \red{x=6}x=6start color #df0030, x, equals, 6, end color #df0030.
Hint #55 / 7
The maximum value of \blue{y}ystart color #6495ed, y, end color #6495ed occurs at the top of the bump in the graph. The coordinates of the top of the bump are (\red{4},\blue{2})(4,2)left parenthesis, start color #df0030, 4, end color #df0030, comma, start color #6495ed, 2, end color #6495ed, right parenthesis. Therefore, the maximum value is \blue{y=2}y=2start color #6495ed, y, equals, 2, end color #6495ed, and it occurs when \red{x=4}x=4start color #df0030, x, equals, 4, end color #df0030.
Hint #66 / 7
The graph of the function is above the xxx-axis for values of \red{x}xstart color #df0030, x, end color #df0030 between \red{x=2}x=2start color #df0030, x, equals, 2, end color #df0030 and \red{x=6}x=6start color #df0030, x, equals, 6, end color #df0030. For these values of \red{x}xstart color #df0030, x, end color #df0030, the function value y\geq 0y≥0y, is greater than or equal to, 0.
Hint #77 / 7
We can now complete the sentences:
This is the graph of a {\text{nonlinear function}}nonlinear functionstart text, n, o, n, l, i, n, e, a, r, space, f, u, n, c, t, i, o, n, end text.
The yyy-intercept of the graph is the function value y={{-6}}y=−6y, equals, minus, 6.
The xxx-intercepts of the graph are located at x={2}x=2x, equals, 2 and x={6}x=6x, equals, 6.
The greatest value of yyy is y={2}y=2y, equals, 2, and it occurs when x={4}x=4x, equals, 4.
For xxx between x=2x=2x, equals, 2 and x=6x=6x, equals, 6, the function value {y \, {\geq } 0}y≥0y, is greater than or equal to, 0.
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