Which of the following functions has a rate of change that stays the same?
A. y equals one third x squared
B. y equals 2 superscript x baseline
C. y equals negative 7 x plus 9
D. y equals x squared plus 1
C. y equals negative 7x plus 9
How many real number solutions does the equation have?
0 equals negative 4 x squared plus 7 x plus 8
A. two solutions
B. one solution
C. no solutions
D. infinitely many solutions
A. two solutions
To determine which function has a rate of change that stays the same, we need to examine the coefficients of the variable x in each function. The rate of change is the slope of the line or the coefficient of x in a linear equation.
Let's analyze each function:
A. y equals one third x squared
In this function, the coefficient of x is 1/3. The rate of change is not constant because it depends on the value of x. As x increases, the rate of change also changes.
B. y equals 2 raised to the power of x
This function represents exponential growth. The rate of change is not constant because the function is exponential, which means it keeps increasing at an accelerating rate as x increases.
C. y equals negative 7x plus 9
This function is a linear equation in the form y = mx + b, where m represents the coefficient of x. In this case, the coefficient of x is -7, which means the rate of change (slope) is -7. The rate of change remains constant regardless of the value of x.
D. y equals x squared plus 1
In this function, the coefficient of x is 0 because there is no x term with a coefficient. Since the coefficient is 0, the rate of change is also 0. This means the function is constant and doesn't change with respect to x.
Therefore, the function in which the rate of change stays the same is option C, y equals negative 7x plus 9.