Which of the following functions has a rate of change that stays the same?
A)y = x2 – 5x –14
B)y = 19x – 10
C)y = 5x
D)y = 0.03x2 + 11x + 1
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the derivative is constant in B and C
To determine which function has a rate of change that stays the same, we need to analyze the coefficients of the x term in each equation. The rate of change refers to how much the y-value changes when the x-value changes by a specific amount.
A) y = x^2 - 5x -14
In this equation, the coefficient of the x term is -5. This means that for every 1 unit increase in x, the y-value will decrease by 5. Therefore, the rate of change is not constant.
B) y = 19x - 10
In this equation, the coefficient of the x term is 19. This means that for every 1 unit increase in x, the y-value will increase by 19. Therefore, the rate of change is constant.
C) y = 5x
In this equation, the coefficient of the x term is 5. This means that for every 1 unit increase in x, the y-value will increase by 5. Therefore, the rate of change is constant.
D) y = 0.03x^2 + 11x + 1
In this equation, the coefficient of the x term is 11. This means that for every 1 unit increase in x, the y-value will increase by 11. Therefore, the rate of change is not constant.
Therefore, the functions B) y = 19x - 10 and C) y = 5x have a rate of change that stays the same.