Key features of an exponential graph | Maths | Quizalize & Oak National Academy

Starter quiz

$y=2^x$ will form __________ graph.

a linear

a quadratic

a reciprocal

an exponential ✓
In the graph of $y=({1\over4})^x$ , what is the value of $y$ when $x=0$ ?

$1\over4$

$0$

$1$ ✓

$4$
In the graph of $y=5^x$ , what is the value of $y$ when $x=-2$ ?

$25$

$-25$

$1\over25$ ✓

$-10$
Which statements are true for ${1\over2}^{100}$ ?

It is greater than $1\over2$

It is less than $1\over2$ ✓

It is very close to 0 ✓

It is very close to 1
$Here is a table of values for <Math>y=5^{-x}</Math>. The missing value is <span class="blank">______</span>.$

Here is a table of values for $y=5^{-x}$ . The missing value is ______.

'25' ✓
Which of these could be the equation of this curve?

$y=4^x$

$y=-4^x$

$y=4^{-x}$ ✓

$y=-4^{-x}$

The general form for an ______ equation is $y = ab^x$ .

'exponential' ✓
Select the statements that are true for the graph of $y = 10^x$ .

The point (0, 1) lies on the curve. ✓

The point (1, 0) lies on the curve.

The point (1, 10) lies on the curve. ✓

The $y$ values decrease rapidly as the $x$ values increase.

The $y$ values increase rapidly as the $x$ values increase. ✓
Laura draws the graphs of $y=5^(-x)$ and $y=5^x$ on the same pair of axes. Which of these statements are correct.

The $x$ -axis an asymptote to both curves. ✓

The $y$ -axis an asymptote to both curves.

The curves are symmetrical about the $x$ -axis.

The curves are symmetrical about the $y$ -axis. ✓
Select the statements that are true for the graph of $y = 0.5^x$ .

The $y$ axis is an asymptote

The $y$ values decrease as the $x$ values increase. ✓

The point (1, 0) lies on the curve.

The point (0, 1) lies on the curve. ✓

The point (-1, -0.5) lies on the curve.
Match each exponential curve to its asymptote.

$y=2^x-3$

⇔

$y=-3$ ✓

$y=3^x-2$

⇔

$y=-2$ ✓

$y=2-3^x$

⇔

$y=2$ ✓

$y=2^x+3$

⇔

$y=3$ ✓
Which of these could be the equation of this curve?

$y=10^x+10$

$y=10^{-x}+10$

$y=10^{-x}-10$

$y=10^x-10$ ✓

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$y=b^x$ will reach zero; the curve will touch the $x$ axis eventually.

Get pupils to input large absolute $x$ values to appreciate that no matter how small the $y$ value it is still a fraction greater than zero.

Exponential - The general form for an exponential equation is y = ab^x where a is the coefficient, b is the base and x is the exponent.
Asymptote - An asymptote is a line that a curve approaches but never touches.