A. plot the data for the functions ƒ(x) and g(x) on a grid. b. identify each function as linear, quadratic, or exponential, and use complete sentences to explain your choices. c. describe what happens to the function values in each function as x increases from left to right. d. at what value(s) of x are the function values equal? if you cannot give exact values for x, give estimates.
A function is linear if it has a constant, additive rate of change for consecutive inputs. A function is exponential if it has a constant, multiplicative rate of change for consecutive inputs.
A function is linear if it has a constant, additive rate of change for consecutive inputs. A function is exponential if it has a constant, multiplicative rate of change for consecutive inputs. A quadratic function does not have a constant rate of change, but it is symmetric on each side of the vertex.
That is the exact answer
Linear function is a function which graph is a straight line,
According to the given graph,
Function f(x) is not a line,
Hence, it can not be a linear function.
The quadratic function is a curved function which has two roots that is its graph has two coordinate intercept.
But f(x) has three roots ( by the graph )
That's why it can not be quadratic function.
The cubic function is also a curved function that has three roots,
And, f(x) has three roots ( shown in the graph)
⇒ It is a cubic function.
Exponential or logarithm function is a function that shows exponential growth or decay.
But f(x) is not growing or decaying exponentially.
That's why it is not an exponential or logarithm function.
Algebraically, linear functions are polynomial functions with a highest exponent of one, exponential functions have a variable in the exponent, and quadratic functions are polynomial functions with a highest exponent of two.
f(x) is quadratic. g(x) and h(x) are linear.
So we have the three functions:
Linear functions are polynomials in which the highest degree is 1.
Quadratic functions are polynomials in which the highest degree is 2.
And exponential functions usually have a variable in the exponent (e.g. 2^x).
For f(x), the highest degree is 2. Thus, f(x) is a quadratic function.
For g(x), the highest degree is 1 and there are no variables in the exponent. Thus, g(x) is a linear function.
Similarly, for h(x), the highest degree is 1 and there are no variables in the exponents, so h(x) is also a linear function.
The plot for the function f(x) and g(x) is attached. The purple curve represents f(x) and the black line represents g(x).
The graph of f(x) shows that f(x) is an exponential function.
The graph of g(x) shows that g(x) is a linear function.
As x increases from left to right, the function f(x) increases very rapidly.
As x increases from left to right, the function f(x) increases at a constant rate.
From the graph it can be seen than the valus of x for which the values of the function are equal are: x = -4 and x = 1.19.
I hope this helps
the first should be quadratic
the second one should be exponential
and the third should be linear
A quadratic function has one point where is switches from going up to going down (or down to up), but this has two, so that's not it.
A cubic function has 2 points where it goes from down to up or up to down, so this may just work.
An exponential function has a constant to the power of something, so it's either staying constantly up or down after 0 or jumping up and down with every x value, which it isn't doing.
Logarithmic functions are similar to exponential functions in that it usually stays either going up or down the whole time.
Using our definitions, a cubic function is the only one that fits
third is linear