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Common Core Standard HSA-REI.D.11 Questions

Explain why the x-coordinates of the points where the graphs of the equations y = f(x) and y = g(x) intersect are the solutions of the equation f(x) = g(x); find the solutions approximately, e.g., using technology to graph the functions, make tables of values, or find successive approximations. Include cases where f(x) and/or g(x) are linear, polynomial, rational, absolute value, exponential, and logarithmic functions.

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Grade 10 Functions and Relations CCSS: HSA-REI.D.11
The functions f(x)=2x3-6x2-(232)x+18 and g(x)=12x+2 are graphed on the same axes. Which of the following are true statements about the system of equations y=f(x),y=g(x)? There may be multiple correct answers.
  1. (1,52) is a solution since it lies on the graph of both functions.
  2. The points (-1,432),(0,18), and (2,3) are solutions because they lie on the graph of one or the other function.
  3. (3,72) is a solution since g(3)=72.
  4. The points (-2,1) and (4,4) are solutions since f(-2)=g(-2) and f(4)=g(4).
Grade 10 Functions and Relations CCSS: HSA-REI.D.11
The functions f(x)=3x2-5x-2 and g(x)=2x2-2x+8 are graphed on the same set of axes. What is true about the points of intersection of the two functions? Choose all correct answers.
  1. Without seeing the graph, there is no way to determine if there are any intersection points.
  2. The intersection points occur where f(x)=g(x).
  3. f(5)=48 and g(5)=48, so 5 is an x-coordinate of a point where the two functions intersect.
  4. f(0)=-2 and g(-2)=20, so (0,20) is a point of intersection.
Grade 11 Functions and Relations CCSS: HSA-REI.D.11
You graph two functions, f(x) and g(x), and they intersect in three places. Which of the following statements MUST be correct?
  1. Neither function is linear.
  2. Solving f(x)=x or g(x)=x will give the x-coordinate of the points of intersection.
  3. There are three distinct x values for which f(x)=g(x).
  4. There are three distinct y values, or output values, for which f(x)=g(x).
Grade 10 Functions and Relations CCSS: HSA-REI.D.11

This question is a part of a group with common instructions. View group »

In order to get a more precise location of the point of intersection, she decides to try the value of x in the middle of the interval. What are the values of each function at this point, rounded to two decimal places?
  1. f(-3)=-6.00,  g(-3)=-7.00
  2. f(-3)=-78.00,  g(-3)=-7.00
  3. f(-3)=-78.00,  g(-3)=-0.39
  4. f(-3)=0.00,  g(-3)=-6.86
Grade 11 Functions and Relations CCSS: HSA-REI.D.11

This question is a part of a group with common instructions. View group »

Given the values of the functions at x=-3, and the relative values of f(x) and g(x) near this point, should Simone choose a value greater than or less than x=-3 to get a more precise value of the point of intersection?
  1. Neither, x=-3 is the point of intersection.
  2. Less than, since f(-3)>g(-3).
  3. Greater than, since f(-3)>g(-3).
  4. Either, since it is still just an approximation.
Grade 11 Functions and Relations CCSS: HSA-REI.D.11

This question is a part of a group with common instructions. View group »

If Simone continues to choose values of x in the middle of each new interval (for example, she would choose x=-2.5 if she looks in the interval -3<x<-2), what would be a reasonable criterion for believing that she has found an accurate point of intersection and why?
  1. |f(x)| is very small, because the x value is very precise.
  2. |g(x)| is very small, since x is near the middle of the interval.
  3. |f(x)+g(x)|2 is near zero, as you've averaged the absolute value of the functions and the functions should cancel each other out.
  4. |f(x)-g(x)| is very small, since these values should be almost equal near the point of intersection.

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