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A function, f(x), passes through the point (0,2). Another function is represented by the equation g(x)=x^2−2x−3. What is the y-intercept of g(x) and which function has the greater y-intercept

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Answer:

  • The y-intercept of function f(x) is 2.
  • The y-intercept of function g(x) is -3.

Therefore, we conclude that function f(x) has a greater y-intercept.

Step-by-step explanation:

The y-intercept of any function can be determined by checking the value of y at x = 0.

Important Tip

  • A point where the graph meets the y-axis — y-intercept.

Determining the y-intercept of the function f(x)

Given the function f(x) passes through the point (0,2).

It means at x = 0, the value of y = 2

Thus, the y-intercept of function f(x) is 2.

Determining the y-intercept of the function g(x)

Given the function g(x)

[tex]g\left(x\right)=x^2-2x-3[/tex]

substitute x = 0 in the function equation

[tex]g\left(0\right)=\left(0\right)^2-2\left(0\right)-3[/tex]

[tex]g\left(0\right)=0-0-3[/tex]

[tex]g\left(0\right)=-3[/tex]

It means at x = 0, the value of y = -3

Thus, the y-intercept of function g(x) is -3.

Conclusion:

  • The y-intercept of function f(x) is 2.
  • The y-intercept of function g(x) is -3.

As 2 > -3

Therefore, we conclude that function f(x) has a greater y-intercept.

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