big145

Why do the graphs of reciprocals of linear functions always have vertical asymptotes, but the graphs of reciprocals of quadratic functions sometimes do not? Justify with an example.

Write an equation to represent a rational function with the following conditions: - reciprocal of a quadratic function - asymptotes with the equations x = -5, x= 4/3, and y = 0 - y < 0 whenever x < -5 - y-intercept of 1.5

The water depth in a harbor is 12m at high tide and 4m at low tide. One cycle is completed every 12 hours. a) Sketch the graph comparing the depth of the water and time for a 24-hour period, starting a low tide. b) Determine an equation of a cosine functi...

Does sin 𝛑/2 = 1/2sin𝛑? Explain your reasoning.

Can a quadratic trigonometric equation have no real solutions? Provide an example to support your opinion.

Explain how many solutions the following trigonometric equation should have: 2cos^2x - 1 = 0, when 0 ≤ x ≤ 2𝛑

A 320g sample of a substance called Iodine-131 is stored in a laboratory for 40 days. At the end of this period, only 7.5g remains. What is the half-life of Iodine-131?

Johnny says you cannot determine the value of log3(9) because there is no meaning. Samira says she can find a value for log-3(9). Explain who is correct and justify your reasoning.