Question
3.) Which function matches the graph above?In a complete sentence on your "work page", explain how to use the zeros of the graph to write the function. (10 points)Responsesf(x) = (x-4)2(x+1)f(x) = (x-4) 2 (x+1)f(x) = (x+4)2(x-1)f(x) = (x+4) 2 (x-1)f(x) = (x+5)2(x-1)f(x) = (x+5) 2 (x-1)f(x)=(x+4)(x-1)
Answers
GPT-4o mini
To determine which function matches the graph you are referring to, we need to identify the zeros (or x-intercepts) of the graph. The zeros can be deduced from the factors in the function form, where each factor corresponds to a zero of the graph.
For example, if the graph has a zero at \( x = 4 \) with a multiplicity of 2, it would indicate that the factor \( (x - 4)^2 \) is present in the function. Similarly, if there is a zero at \( x = -1 \), then the factor \( (x + 1) \) would be included.
By analyzing the zeros visually on the graph, we can match them with the appropriate function from the options listed. If we see that the graph intersects the x-axis at \( x = 4 \) and touches it (indicating a multiplicity of 2), and also intersects at \( x = -1 \), the corresponding function would be:
\( f(x) = (x - 4)^2(x + 1) \)
Therefore, in constructing the function using the zeros of the graph, identify each x-intercept and its multiplicity to write the corresponding factors, which when multiplied together will give the overall function.
For example, if the graph has a zero at \( x = 4 \) with a multiplicity of 2, it would indicate that the factor \( (x - 4)^2 \) is present in the function. Similarly, if there is a zero at \( x = -1 \), then the factor \( (x + 1) \) would be included.
By analyzing the zeros visually on the graph, we can match them with the appropriate function from the options listed. If we see that the graph intersects the x-axis at \( x = 4 \) and touches it (indicating a multiplicity of 2), and also intersects at \( x = -1 \), the corresponding function would be:
\( f(x) = (x - 4)^2(x + 1) \)
Therefore, in constructing the function using the zeros of the graph, identify each x-intercept and its multiplicity to write the corresponding factors, which when multiplied together will give the overall function.