The graph of ℎ in the figure has vertical asymptotes at x=−2 and x=3. Analyze the following limits. <IMAGE>
lim x→−2^+ h(x)

Verified step by step guidance

1. Step 1: Understand the concept of a vertical asymptote. A vertical asymptote at x = a means that as x approaches a, the function h(x) tends to infinity or negative infinity.
2. Step 2: Identify the direction of approach. The limit x → -2^+ indicates that we are approaching x = -2 from the right side (values greater than -2).
3. Step 3: Analyze the behavior of h(x) as x approaches -2 from the right. Since there is a vertical asymptote at x = -2, observe whether h(x) increases towards positive infinity or decreases towards negative infinity.
4. Step 4: Use the graph to determine the behavior. Look at the graph of h(x) near x = -2 from the right side to see if the function is going upwards or downwards.
5. Step 5: Conclude the limit based on the observed behavior. If h(x) goes to positive infinity, the limit is positive infinity. If it goes to negative infinity, the limit is negative infinity.