Question

ii. intercepts of a graph
an x - intercept is written as the ordered pair _, and a y - intercept is written as the ordered pair _.
to identify the x - intercepts of a graph, ...
to identify the y - intercepts of a graph, ...
iii. symmetry
the three types of symmetry that a graph can exhibit are ...
knowing the symmetry of a graph before attempting to sketch it is helpful because ...
a graph is symmetric with respect to the y - axis if, whenever (x,y) is on the graph, _ is also on the graph. a graph is symmetric with respect to the x - axis if, whenever (x,y) is on the graph, _ is also on the graph. a graph is symmetric with respect to the origin if, whenever (x,y) is on the graph, _ is also on the graph.

Explanation:

1. For \(x\)-intercepts, \(y = 0\) on the \(x\)-axis; for \(y\)-intercepts, \(x=0\) on the \(y\)-axis.
2. In \(y\)-axis symmetry, \(x\) - coordinate changes sign; in \(x\)-axis symmetry, \(y\) - coordinate changes sign; in origin - symmetry, both \(x\) and \(y\) coordinates change sign.

Answer:

1. An \(x\)-intercept is written as the ordered pair \((x,0)\), and a \(y\)-intercept is written as the ordered pair \((0,y)\).
2. A graph is symmetric with respect to the \(y\)-axis if, whenever \((x,y)\) is on the graph, \((-x,y)\) is also on the graph. A graph is symmetric with respect to the \(x\)-axis if, whenever \((x,y)\) is on the graph, \((x, -y)\) is also on the graph. A graph is symmetric with respect to the origin if, whenever \((x,y)\) is on the graph, \((-x,-y)\) is also on the graph.