Question

matching the meaning of key features of a graph
match the key aspect of a function’s graph with its meaning
intervals of the domain where the
graph is below the x-axis
intervals of the domain where the
graph is above the x-axis
location on graph where input is zero
location on graph where output is zero
x-intercept
y-intercept
f(x) > 0
f(x) < 0

Explanation:

• x - intercept: By definition, the x - intercept of a function \(y = f(x)\) is the point where the output \(y=f(x) = 0\). So it matches with "location on graph where output is zero".
• y - intercept: The y - intercept occurs when the input \(x = 0\) (since we are looking at the value of the function when \(x = 0\)). So it matches with "location on graph where input is zero".
• \(f(x)>0\): When \(f(x)>0\), the value of the function (the y - value) is positive. On the graph of the function, this corresponds to the intervals of the domain where the graph is above the \(x\) - axis (because above the \(x\) - axis, \(y>0\)).
• \(f(x)<0\): When \(f(x)<0\), the value of the function (the y - value) is negative. On the graph of the function, this corresponds to the intervals of the domain where the graph is below the \(x\) - axis (because below the \(x\) - axis, \(y < 0\)).

Answer:

• \(x\) - intercept: location on graph where output is zero
• \(y\) - intercept: location on graph where input is zero
• \(f(x)>0\): intervals of the domain where the graph is above the \(x\) - axis
• \(f(x)<0\): intervals of the domain where the graph is below the \(x\) - axis