The following figure shows the graph of a function h ....

The following figure shows the graph of a function $h$ . (GRAPH CAN'T COPY) (a) Find $h(a), h(b), h(c),$ and $h(d)$ (b) Is $h(0)$ positive or negative? (c) For which values of $x$ does $h(x)=0 ?$ (d) Which is larger, $h(b)$ or $h(0) ?$ (e) As $x$ increases from $c$ to $d$, do the corresponding values of $h(x)$ increase or decrease? (f) As $x$ increases from $a$ to $b$, do the corresponding values of $h(x)$ increase or decrease?

The following figure shows the graph of a function $h$ . (GRAPH CAN'T COPY)
(a) Find $h(a), h(b), h(c),$ and $h(d)$
(b) Is $h(0)$ positive or negative?
(c) For which values of $x$ does $h(x)=0 ?$
(d) Which is larger, $h(b)$ or $h(0) ?$
(e) As $x$ increases from $c$ to $d$, do the corresponding values of $h(x)$ increase or decrease?
(f) As $x$ increases from $a$ to $b$, do the corresponding values of $h(x)$ increase or decrease?

Key Concepts

Comparison of Function Values

This concept is about assessing and comparing the magnitudes of output values at different input values. It is important when determining which of two function values, such as h(b) versus h(0), is larger, and involves careful observation of the graph's vertical positioning at those points.

Increasing and Decreasing Behavior

This concept relates to analyzing the trend of a function. When moving along the x-axis, if the graph moves upward, the function is increasing; if it moves downward, the function is decreasing. Establishing these trends helps answer questions about the behavior of the function over specific intervals.

Positive and Negative Values

This concept involves determining whether the output of a function is above or below the x-axis. If the graph is above the x-axis, the function’s value is positive; if below, it is negative. This understanding is crucial when establishing whether h(0) is positive or negative.

Graph Interpretation

This concept involves understanding and analyzing the visual representation of a function. It includes reading coordinate points on the graph, such as identifying the input value (x-coordinate) and the corresponding output value (y-coordinate), and determining features like intercepts and relative positions of points on the graph.

Function Evaluation

This concept entails computing the value of a function at given inputs. It is done by looking at the graph to determine the output that corresponds to the given input and is fundamental when answering questions related to specific points such as h(a), h(b), etc.

Identifying Zeros of a Function

Determining the zeros of a function involves finding the input values where the function’s output equals zero. On a graph, these are the points where the graph intersects the x-axis, making it an essential concept when solving for h(x) = 0.