Determine algebraically whether or not the function f left parenthesis x right parenthesis equals negative x cubed minus 2 x squared plus 5 is even or odd, and justify your answer.
(1 point)
Responses
The function is odd because f left parenthesis negative x right parenthesis equals negative f left parenthesis x right parenthesis.
The function is odd because Image with alt text: f left parenthesis negative x right parenthesis equals negative f left parenthesis x right parenthesis .
The function is odd because f left parenthesis negative x right parenthesis equals f left parenthesis x right parenthesis.
The function is odd because Image with alt text: f left parenthesis negative x right parenthesis equals f left parenthesis x right parenthesis .
The function is even because f left parenthesis negative x right parenthesis equals negative f left parenthesis x right parenthesis.
The function is even because Image with alt text: f left parenthesis negative x right parenthesis equals negative f left parenthesis x right parenthesis .
The function is even because f left parenthesis negative x right parenthesis equals f left parenthesis x right parenthesis.
The function is even because Image with alt text: f left parenthesis negative x right parenthesis equals f left parenthesis x right parenthesis .
The function is neither even nor odd because f left parenthesis negative x right parenthesis not-equals f left parenthesis x right parenthesis and f left parenthesis negative x right parenthesis not-equals negative f left parenthesis x right parenthesis.
The correct answer is: The function is odd because f(left parenthesis negative x right parenthesis) equals negative f(left parenthesis x right parenthesis).
Which of the following functions are odd? Select all that apply.
(1 point)
Responses
f left parenthesis x right parenthesis equals 7 x superscript 5 baseline minus 4 x
Image with alt text: f left parenthesis x right parenthesis equals 7 x superscript 5 baseline minus 4 x
f left parenthesis x right parenthesis equals 3 x squared minus 9 x
Image with alt text: f left parenthesis x right parenthesis equals 3 x squared minus 9 x
f left parenthesis x right parenthesis equals 6 x superscript 7 baseline plus 4 x cubed minus 2
Image with alt text: f left parenthesis x right parenthesis equals 6 x superscript 7 baseline plus 4 x cubed minus 2
f left parenthesis x right parenthesis equals negative 5 x superscript 9 baseline plus 8 x superscript 5 baseline plus 4 x cubed
Image with alt text: f left parenthesis x right parenthesis equals negative 5 x superscript 9 baseline plus 8 x superscript 5 baseline plus 4 x cubed
f left parenthesis x right parenthesis equals 2 x cubed plus 5
The functions that are odd are:
1) f(x) = 7x^5 - 4x
2) f(x) = 3x^2 - 9x
4) f(x) = -5x^9 + 8x^5 + 4x^3
The function is odd because f(left parenthesis negative x right parenthesis) equals negative f(left parenthesis x right parenthesis).
Fresnel integrals are functions that describe how light bends, and they are often used in the design of highways, railroads, and roller coasters. The graph shown is an approximation of the Fresnel integral. Use the graph to determine which of the following statements about the function is true.
A function is graphed on a coordinate plane.A function is graphed on a coordinate plane. The x-axis goes from negative 5 to 5 and the y-axis goes from negative 1 to 1. The graph is a wave that starts oscillating on the negative x-axis, passes through the origin, then continues to oscillate on the positive x-axis. The height of each wave increases the closer the function gets to the origin. The wave is symmetrical around the point left parenthesis 0 comma 0 right parenthesis.
(1 point)
Responses
The function is even.
The function is even.
The function is odd.
The function is odd.
The function is neither even nor odd.
The function is neither even nor odd.
The function is both even and odd.
The correct answer is: The function is neither even nor odd.
Which of the following graphs represents an even function?
(1 point)
Responses
A graph is shown on the coordinate plane. The graph is a curve that increases from negative infinity to the point left parenthesis negative 1.095 comma 1.051 right parenthesis, then decreases through the origin to point left parenthesis 1.095 comma negative 1.051 right parenthesis and then increases to infinity.
Image with alt text: A graph is shown on the coordinate plane. The graph is a curve that increases from negative infinity to the point left parenthesis negative 1.095 comma 1.051 right parenthesis, then decreases through the origin to point left parenthesis 1.095 comma negative 1.051 right parenthesis and then increases to infinity.
A graph is shown on the coordinate plane.The graph is a continuous curve that decreases from infinity to a cusp at the point left parenthesis negative 1.316 comma 0 right parenthesis, then increases to the point left parenthesis negative 0.88 comma 2.112 right parenthesis, then decreases to a cusp at the origin, then increases to the point left parenthesis 0.88 comma 2.112 right parenthesis, then decreases to a cusp at the point left parenthesis 1.316 comma 0 right parenthesis, then increases to infinity.
Image with alt text: A graph is shown on the coordinate plane. The graph is a continuous curve that decreases from infinity to a cusp at the point left parenthesis negative 1.316 comma 0 right parenthesis, then increases to the point left parenthesis negative 0.88 comma 2.112 right parenthesis, then decreases to a cusp at the origin, then increases to the point left parenthesis 0.88 comma 2.112 right parenthesis, then decreases to a cusp at the point left parenthesis 1.316 comma 0 right parenthesis, then increases to infinity.
A graph is shown on the coordinate plane.The graph is a rational function consisting of three curves. The first curve increases from negative infinity to the point left parenthesis negative 0.684 comma negative 1.223 right parenthesis then decreases to negative infinity. The second curve decreases from infinity to the point left parenthesis 0.628 comma 1.789 right parenthesis then increases to infinity. The third curve increases from negative infinity to positive infinity. The graph has asymptotes at x = 0, x = 2, and y = x.
Image with alt text: A graph is shown on the coordinate plane. The graph is a rational function consisting of three curves. The first curve increases from negative infinity to the point left parenthesis negative 0.684 comma negative 1.223 right parenthesis then decreases to negative infinity. The second curve decreases from infinity to the point left parenthesis 0.628 comma 1.789 right parenthesis then increases to infinity. The third curve increases from negative infinity to positive infinity. The graph has asymptotes at x = 0, x = 2, and y = x.
A graph is shown on the coordinate plane. The graph is a parabola that opens right with a vertex at left parenthesis 0 comma 0 right parenthesis.
The graph that represents an even function is:
A graph is shown on the coordinate plane. The graph is a parabola that opens right with a vertex at left parenthesis 0 comma 0 right parenthesis.
dont ue this i got 0/4
I apologize for the confusion. Let's go through the options again:
1) A graph is shown on the coordinate plane. The graph is a curve that increases from negative infinity to the point (-1.095, 1.051), then decreases through the origin to the point (1.095, -1.051) and then increases to infinity.
2) A graph is shown on the coordinate plane. The graph is a continuous curve that decreases from infinity to a cusp at the point (-1.316, 0), then increases to the point (-0.88, 2.112), then decreases to a cusp at the origin, then increases to the point (0.88, 2.112), then decreases to a cusp at the point (1.316, 0), then increases to infinity.
3) A graph is shown on the coordinate plane. The graph is a rational function consisting of three curves. The first curve increases from negative infinity to the point (-0.684, -1.223) then decreases to negative infinity. The second curve decreases from infinity to the point (0.628, 1.789) then increases to infinity. The third curve increases from negative infinity to positive infinity. The graph has asymptotes at x = 0, x = 2, and y = x.
4) A graph is shown on the coordinate plane. The graph is a parabola that opens right with a vertex at (0, 0).
Based on the characteristics of an even function, an even function exhibits symmetry with respect to the y-axis. Looking at the options, only option 4) represents a parabola that opens right with a vertex at (0, 0). This indicates that the function is symmetrical about the y-axis and therefore, it is an even function.
So the graph that represents an even function is the one described in option 4).