The graph of [tex]y = {\log _b}\left( x \right) + 4[/tex] is the graph of [tex]y = {\log _b}x[/tex] translated 4 units up is true. Option (c) is correct.
Further explanation:
Given:
The statements are as follows,
(a). The graph of [tex]y = {\log _b}\left( {x - 4} \right)[/tex] is the graph of [tex]y = {\log _b}x[/tex] translated 4 units down.
(b). The graph of [tex]y = {\log _b}\left( x \right) - 4[/tex] is the graph of [tex]y = {\log _b}x[/tex] translated 4 units left.
(c). The graph of [tex]y = {\log _b}\left( x \right) + 4[/tex] is the graph of [tex]y = {\log _b}x[/tex] translated 4 units up.
(d). The graph of [tex]y = {\log _b}\left( {x + 4} \right)[/tex] is the graph of [tex]y = {\log _b}x[/tex] translated 4 units right.
Explanation:
The rules of translation are as follows,
1. [tex]f\left( x \right) + c[/tex] can be obtained by shifting the graph of [tex]f\left( x \right) c[/tex] units upward.
2. [tex]f\left( x \right) - c[/tex] can be obtained by shifting the graph of [tex]f\left( x \right) c[/tex] units downward.
3. [tex]f\left( {x - c} \right)[/tex] can be obtained by shifting the graph of [tex]f\left( x \right) c[/tex] units right.
4. [tex]f\left( {x + c} \right)[/tex] can be obtained by shifting the graph of [tex]f\left( x \right) c[/tex] units left.
According to the rules of translation the statement (a) is not correct.
According to the rules of translation the statement (a) is not correct.
According to the rules of translation the statement (c) is correct.
According to the rules of translation the statement (a) is not correct.
The graph of [tex]y = {\log _b}\left( x \right) + 4[/tex] is the graph of [tex]y = {\log _b}x[/tex] translated 4 units up is true. Option (c) is correct.
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Answer details:
Grade: Middle School
Subject: Mathematics
Chapter: Triangles
Keywords: translation, transformation, 4 units upward, 4 units downward, true, left, right, graph, logarithm function, statement.
