Logarithmic and Exponential Functions

The video tutorial by Mr. Ish covers three types of function graphs: absolute value, exponential, and logarithmic. It begins with an introduction to the types of graphs discussed, followed by a detailed exploration of absolute value graphs, including their properties, symmetry, and transformations. The tutorial then moves on to exponential function graphs, explaining their basic form, reflections, and vertical shifts. Finally, the video examines logarithmic function graphs, focusing on their asymptotes, reflections, and horizontal shifts. Throughout, the video emphasizes the beauty and complexity of these mathematical graphs.

What types of graphs are discussed in the video?

• Absolute value, exponential, and logarithmic functions

• Hyperbolic, circular, and elliptical functions

• Trigonometric, polynomial, and rational functions

• Linear, quadratic, and cubic functions

What is the basic shape of an absolute value graph?

• A straight line

• A parabola

• A V-shape

• A circle

How does the graph of |x - h| differ from |x|?

• It shifts left by h units

• It shifts right by h units

• It shifts down by h units

• It shifts up by h units

What happens to an absolute value graph when a coefficient greater than 1 is applied?

• The graph shifts horizontally

• The graph compresses vertically

• The graph stretches vertically

• The graph reflects across the x-axis

What is the basic form of an exponential function?

• f(x) = x^2

• f(x) = |x|

• f(x) = e^x

• f(x) = log(x)

Where does the basic exponential graph intersect the y-axis?

• (0, 1)

• (1, 1)

• (0, 0)

• (1, 0)

How can you reflect an exponential graph across the y-axis?

• By multiplying the exponent by -1

• By dividing the exponent by a constant

• By subtracting a constant from the exponent

• By adding a constant to the exponent

What is the basic form of a logarithmic function?

• f(x) = |x|

• f(x) = x^2

• f(x) = log(x)

• f(x) = e^x

Where does the basic logarithmic graph intersect the x-axis?

• (1, 0)

• (0, 1)

• (0, 0)

• (1, 1)

What happens to the asymptote of a logarithmic graph when it is shifted horizontally?

• It remains unchanged

• It disappears

• It moves vertically

• It moves horizontally