Original
Here we have unlabeled graphs of {{MATH_167}}, {{MATH_168}}, and {{MATH_169}}:
{{CMD_170}}
{{ENV_171}}
{{CMD_172}}
Identify each curve above as a graph of {{MATH_173}}, {{MATH_174}}, or {{MATH_175}}.
{{CMD_176}}
Here we see three curves, {{MATH_177}}, {{MATH_178}}, and {{MATH_179}}. Since {{MATH_180}} is
{{CMD_181}}{{CMD_182}}positive{{CMD_183}} {{CMD_184}}negative{{CMD_185}}
{{CMD_186}}increasing{{CMD_187}} {{CMD_188}}decreasing{{CMD_189}}{{CMD_190}} when {{MATH_191}} is
positive and
{{CMD_192}}{{CMD_193}}positive{{CMD_194}}{{CMD_195}}negative{{CMD_196}}{{CMD_197}}increasing{{CMD_198}}{{CMD_199}}decreasing{{CMD_200}}{{CMD_201}}
when {{MATH_202}} is negative, we see
{{MATH_203}}
Since {{MATH_204}} is increasing when {{MATH_205}} is
{{CMD_206}}{{CMD_207}}positive{{CMD_208}}{{CMD_209}}negative{{CMD_210}}{{CMD_211}}increasing{{CMD_212}}
{{CMD_213}}decreasing{{CMD_214}}{{CMD_215}} and decreasing when {{MATH_216}} is
{{CMD_217}}{{CMD_218}}positive{{CMD_219}}{{CMD_220}}negative{{CMD_221}}{{CMD_222}}increasing{{CMD_223}}{{CMD_224}}decreasing{{CMD_225}}{{CMD_226}}, we see
{{MATH_227}}
Hence {{MATH_228}}, {{MATH_229}}, and {{MATH_230}}.
{{CMD_231}}
{{CMD_232}}