a Substitute - 1 for x in each instance of the x-variable.
B
b Substitute 0 for x in each instance of the x-variable.
C
c Substitute 1 for x in each instance of the x-variable.
D
d Substitute 12 for f(x) and solve for x.
E
e You will need to substitute 0 and solve, twice.
F
f Substitute 3(2)^x for f(x) and 13x for g(x).
A
a f(- 1)= 3/2
B
b f(0)= 3
C
c f(1)= 6
D
d x=2
E
ex-intercept: Does not exist y-intercept: (0,3)
F
f f(x) * g(x)=2^x/x
Practice makes perfect
a Using the function f(x) we want to evaluate for the given value, f( - 1).
To do this we need to substitute - 1 for x in each instance of the x-variable and simplify.
b Using the function f(x) we want to evaluate for the given value, f( 0).
To do this, we need to substitute 0 for x in each instance of the x-variable and simplify.
c Using the function f(x) we want to evaluate for the given value, f( 1).
To do this, we need to substitute 1 for x in each instance of the x-variable and simplify.
Now, notice that 2 is the value of x that satisfies this equation. It means that x=2 gives f(x)=12.
e The given function is written in function notation. For simplicity let's rewrite it using the y-variable.
f(x)=3(2)^x ⇒ y=3(2)^x
To determine the points where the graph crosses the x- and y-axis, we need to substitute 0 for one variable, solve, then repeat for the other variable.
Finding the x-intercept
Think of the point where the graph of an equation crosses the x-axis. The y-value of that ( x, y) coordinate pair is 0, and the x-value is the x-intercept. To find the x-intercept of the equation we should substitute 0 for y and solve for x.
There is no such value of x such that 2 raised to the power of x will have the value of 0. Thus, our substitution resulted in a contradiction. It means that the given function does not have an x-intercept.
Finding the y-intercept
Let's use the same concept to find the y-intercept. Consider the point where the graph of the equation crosses the y-axis. The x-value of the ( x, y) coordinate pair at the y-intercept is 0. Therefore, substituting 0 for x will give us the y-intercept.
