Which of the following could be the equation of m(x) in factored form, given its graph?
(1 point)
Responses
m(x)=(x+1)(x−3)(x−5)
m left parenthesis x right parenthesis equals left parenthesis x plus 1 right parenthesis left parenthesis x minus 3 right parenthesis left parenthesis x minus 5 right parenthesis
m(x)=(x+1)(x−3)(x−5)(x−15)
m left parenthesis x right parenthesis equals left parenthesis x plus 1 right parenthesis left parenthesis x minus 3 right parenthesis left parenthesis x minus 5 right parenthesis left parenthesis x minus 15 right parenthesis
m(x)=(x−1)(x+3)(x+5)
m left parenthesis x right parenthesis equals left parenthesis x minus 1 right parenthesis left parenthesis x plus 3 right parenthesis left parenthesis x plus 5 right parenthesis
m(x)=(x−1)(x+3)(x+5)(x+15)
m(x)=(x+1)(x−3)(x−5)
To determine the equation of m(x) in factored form, we need to analyze the factors of the graph. Looking at the options provided, the equation that matches the factors of the graph is:
m(x) = (x + 1)(x - 3)(x - 5)
So, the correct option is:
m(x) = (x + 1)(x - 3)(x - 5)
To determine which equation could represent the function m(x) in factored form based on its graph, you need to analyze the behavior of the graph.
1. Look at the x-intercepts: Determine the values of x where the graph crosses or touches the x-axis.
- In the given graph, it appears that the x-intercepts are located at x = -1, x = 3, and x = 5.
2. Use the x-intercepts to identify the factors: For an equation in factored form, each x-intercept corresponds to a factor of the form (x - a), where 'a' is the value of the x-intercept.
- From the x-intercepts provided, the factors would be (x + 1), (x - 3), and (x - 5).
Now, let's compare the provided equations with the determined factors:
A. m(x) = (x + 1)(x - 3)(x - 5)
- This equation matches the determined factors (x + 1), (x - 3), and (x - 5). Hence, it could potentially represent the function m(x) in factored form.
B. m(x) = (x + 1)(x - 3)(x - 5)(x - 15)
- Although this equation has additional factor (x - 15), it is not observed or mentioned in the given graph. Therefore, this equation does not match the provided information.
C. m(x) = (x - 1)(x + 3)(x + 5)
- These factors (x - 1), (x + 3), and (x + 5) do not match the determined x-intercepts (-1, 3, 5). Thus, this equation does not align with the given graph.
D. m(x) = (x - 1)(x + 3)(x + 5)(x + 15)
- Similar to equation B, this equation contains an additional factor (x + 15), which is not indicated in the graph. Therefore, it does not match the given information.
Based on the analysis, equation A, m(x) = (x + 1)(x - 3)(x - 5), is the equation that could represent the function m(x) in factored form according to the graph.