Question

11 multiple choice 1 point which equation represents the function shown in the accompanying graph? 12 multiple choice 1 point to slide the graph of the equation y = 3^x two units left, the equation is altered. what is the new equation?

Explanation:

Step1: Recall vertex - form of absolute - value function

The general form of an absolute - value function is $y=a|x - h|+k$, where $(h,k)$ is the vertex of the graph. For the graph of $y = |x|$, the vertex is $(0,0)$.

Step2: Identify the vertex of the given graph

The vertex of the given graph is $(0, - 1)$.

Step3: Determine the function

For an absolute - value function $y = |x|+k$, when $k=-1$, the function is $y = |x|-1$. So the function for the first graph is $f(x)=|x|-1$.

Step4: Recall the rule for horizontal translation of a function

The rule for translating the graph of $y = f(x)$ $c$ units to the left is $y = f(x + c)$.

Step5: Apply the rule to the exponential function

Given $y = 3^{x}$, to slide it 2 units to the left, we replace $x$ with $x + 2$. So the new function is $y=3^{x + 2}$.

Answer:

1. D. $f(x)=|x|-1$
2. D. $y = 3^{x+2}$