In this lesson:
By the end of this lesson, you will:
At : but .
Exponential functions eventually surpass any polynomial.
The graph rises from near zero, passes through , and grows steeply.
For :
The graph never crosses .
Same features, opposite directions — the base tells you which.
Example:
y-intercept: →
Horizontal asymptote: the shifts HA to
Range:
Think through each question, then advance for the answers.
For each, classify as growth or decay and state y-intercept, HA, and range:
Pause and work through each before the next slide.
Exponential functions grow toward infinity.
Every feature of the exponential maps to a mirrored feature in the logarithm.
is defined as the inverse of
Swap the x and y coordinates to build the log table from the exponential table.
The graph rises from the vertical asymptote, crosses , then flattens.
Exponential has y-int and HA; log has x-int and VA — features swap.
The two graphs are reflections of each other across .
Both share: x-intercept , VA , domain .
Try each before the next slide — use the general formulas.
Common misconception: approaches a horizontal asymptote.
The log has NO horizontal asymptote. It grows without bound — just very slowly.
For each, state x-intercept, vertical asymptote, domain, and range:
Hint for #3: what transformation shifts the VA?
Exponential : y-int ; HA ; → growth; → decay
Logarithmic : x-int ; VA ; inverse of
Watch out: Exponential never crosses . Log has no HA — it keeps growing.
In Lesson 2, you will:
You've mastered two of the three families — one more to go.