which of the following has a rate of change that stays the same
a. y= 4^x ***
b. y= 1/5x^2
c. y= -6x+8
d. y= x^2+3
I think it's a but I'm not sure. Can one of the Jishka teachers check? Thank you!!
The answer is C because the rate of change is always -6.
Yes, like y = m x + b :)
Thank you!!!
Well, isn't it a coincidence that they call me the "Clown Bot" because I have a funny answer for you! So, the rate of change is all about how much a function is changing over a given interval. In this case, the function that has a rate of change that stays the same is... drumroll, please... (c) y = -6x + 8! Why, you ask? Well, because it has a constant slope of -6. The other functions do not have a constant rate of change. But hey, thanks for letting me bring some humor into your day!
To determine which of the given functions has a rate of change that stays the same, we need to identify the function that represents a linear relationship.
The rate of change, also known as the slope, is constant in a linear function. This means that for every unit change in the independent variable (x), the change in the dependent variable (y) remains the same.
Let's analyze each function:
a. y = 4^x: This is an exponential function, not a linear function. The rate of change increases exponentially as x increases. Therefore, it does not have a constant rate of change.
b. y = (1/5)x^2: This is a quadratic function because of the exponent of 2 on x. Quadratic functions do not have a constant rate of change, as the rate of change varies depending on the value of x.
c. y = -6x + 8: This is a linear function in the form of y = mx + b, where m represents the slope. In this case, the slope is -6, which means that for every unit increase in x, y decreases by 6 units. This function has a constant rate of change.
d. y = x^2 + 3: This is another quadratic function since the exponent of x is 2. Like the previous quadratic function, it does not have a constant rate of change.
Therefore, the function with a rate of change that stays the same is c. y = -6x + 8.
Note: If you are unsure about any answer, it's always a good idea to verify with your teacher or another reliable source.