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Algebra 1

4.10.4 Comparing Graphs and Statements that Represent Functions without a Context

Algebra 14.10.4 Comparing Graphs and Statements that Represent Functions without a Context

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Activity

Here are graphs that represent two functions, ff and gg.

A graph with two curves: f, a black upward then downward parabola peaking at y equals 8, and g, a blue straight line sloping downward from y equals 8. The x-axis ranges from 0 to 12, and the y-axis ranges from 0 to 9.

Decide which function value is greater for each given input. Be prepared to explain your reasoning.

1. Which is greater, f(2)f(2) or g(2)g(2)

2. Which is greater, f(4)f(4) or g(4)g(4)

3. Which is greater, f(6)f(6) or g(6)g(6)

4. Which is greater, f(8)f(8) or g(8)g(8)

5. Is there a value of xx at which the equation f(x)=g(x)f(x)=g(x) is true? Be prepared to show your reasoning.

6. Identify at least two values of xx at which the inequality f(x)<g(x)f(x)<g(x) is true.

Self Check

Which of the following is true about the graphs of f ( x ) and g ( x ) below?

GRAPH OF TWO FUNCTIONS. ONE IS A PARABOLA THAT OPENS UP. THE OTHER IS A LINE WITH A NEGATIVE SLOPE. THE FUNCTIONS INTERSECT AT THE POINTS (1, −3) AND (−2, 0).

  1. f ( 1 ) = g ( 1 )
  2. \(f(-3)<g(-3)\)< p=""></g(-3)\)<>
  3. f ( 1 ) = g ( 1 )
  4. f ( 0 ) > g ( 0 )

Additional Resources

Using Graphs to Find Values

Two functions, f(x)f(x) and g(x)g(x), are graphed below.

A graph showing two functions: f(x), a parabola opening upward with a vertex of (negative 4,0) and x-intercepts at negative 2 and 2; and g(x), a straight downward-sloping line. The curves intersect near the points (negative 2, negative 2) and (1, negative 3) on the coordinate plane.

What is the value of f(1)f(1)?

Look at where x=1x=1 touches the graph of ff. The yy-value is –3.

f(1)=3f(1)=3

What is the value of g(1)g(1)?

Look where x=1x=1 touches the graph of gg. The yy-value is –1.

g(1)=1g(1)=1

Which value is greater?

g(1)>f(1)g(1)>f(1)

Try it

Try It: Using Graphs to Find Values

Two functions, f(x)f(x) and g(x)g(x), are graphed below.

Graph showing two functions: f of x, a downward-opening parabola, and g of x, a straight downward-sloping line. Both intersect the y-axis above 0. The axes are labeled, and the curves are named.

Which is greater, f(1)f(1) or g(1)g(1)?

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