Functions and Trig Midterm Exam

The slope of a line is a measure of its steepness, calculated as the rise over run. It can be positive, negative, zero, or undefined.

An undefined slope occurs when a line is vertical, meaning it goes straight up and down, and there is no horizontal change.

As @@x ightarrow - ext{infinity}, h(x) ightarrow - ext{infinity} $$and as$$ x ightarrow ext{infinity}, h(x) ightarrow ext{infinity}@@.

An exponential growth function can be written as $$y = a(1 + r)^x$$ , where $$a$$ is the initial amount, $$r$$ is the growth rate, and $$x$$ is the time.

The axis of symmetry is a vertical line that divides the parabola into two mirror-image halves. For a function in the form $$y = ax^2 + bx + c$$ , it is given by $$x = -\frac{b}{2a}$$ .

The domain of a function is the set of all possible input values (x-values) for which the function is defined.

The range of a function is the set of all possible output values (y-values) that the function can produce.

A polynomial function is a function that can be expressed in the form $$f(x) = a_nx^n + a_{n-1}x^{n-1} + ... + a_1x + a_0$$ , where $$a_n, a_{n-1}, ..., a_0$$ are constants and $$n$$ is a non-negative integer.

Linear functions have a constant rate of change and graph as straight lines, while nonlinear functions have varying rates of change and graph as curves.

The intercepts of a function are the points where the graph intersects the axes: the x-intercept(s) where $$y=0$$ and the y-intercept where $$x=0$$ .