Growth stocks may be among the first to take off in a new bull market. As major indexes touched bear territory last year, many of these stocks suffered the most. Investors often opt for the safest and steadiest of stocks during tough market times. Today, though, some of these beaten-down players represent opportunity for investors. Those with strong businesses and solid long-term outlooks may not only recover -- they also may deliver growth over time.

Two already have been gathering momentum. I'm talking about Amazon (AMZN -0.01%) and Shopify (SHOP 2.95%). Both stocks plummeted last year -- but this year, they're climbing in the double digits. Let's find out more about these two magnificent growth stocks to add to your portfolio right now.

1. Amazon

Amazon sank last year for a few reasons. First, rising inflation drove the company's costs higher -- and also weighed on the wallets of its customers. Amazon sells general merchandise to customers on its e-commerce site and cloud computing services to companies through its Amazon Web Services (AWS) business.

A rapid expansion of its fulfillment network and negative impact from its stock investment in Rivian Automotive also created headwinds.

But the good news is these problems are temporary. And Amazon has taken control of what it can control to recover and grow down the road. The company revamped its cost structure -- an effort that should make it stronger over the long term. Some of the recent efforts include job cuts, shifting investment into the highest growth areas, and improving efficiency across the fulfillment network.

The efforts already are bearing fruit. In the most recent quarter, Amazon reported a double-digit increase in operating cash flow. And it greatly reduced the outflow of cash over the trailing 12 months -- to about $3 billion from more than $18 billion in the year-earlier period.

It's important to remember Amazon is a leader in two high-growth industries. E-commerce and cloud computing services both are growing in the double digits. Amazon should benefit from this as the economy recovers.

Today, Amazon shares are trading for about 2.4 times sales. This is close to their lowest by this measure since 2016. So, even considering Amazon's gains so far this year, the stock remains an excellent buy.

AMZN PS Ratio Chart

AMZN PS Ratio data by YCharts

2. Shopify

Shopify also should benefit from the growth in e-commerce. That's because the company helps other businesses bring their operations online. Shopify sells businesses a full range of e-commerce solutions. These include website creation, product sales, marketing, and behind-the-scenes features like inventory management.

This has brought the company significant earnings growth over time.

SHOP Revenue (Annual) Chart

SHOP Revenue (Annual) data by YCharts

The picture started to darken last year after a venture into fulfillment and delivery weighed on earnings. But Shopify quickly recognized the problem and readjusted. The company recently announced the sale of its logistics business to Flexport. As part of the deal, Shopify gained a 13% stake in the company. And, by making Flexport its logistics partner, Shopify still will benefit from this top-notch logistics service -- but without the costs of owning the operation.

In the most recent quarter, Shopify reported double-digit gains in several key metrics, including gross merchandise volume, total revenue, and gross profit dollars. Importantly, monthly recurring revenue is on the rise. That's thanks to more customers shifting from trials to full plans and more Shopify Plus members using point-of-sale pro solutions.

Today, Shopify trades for about 13 times sales. That's a far cry from levels of about 60 just a few years ago. Meanwhile, thanks to Shopify's expertise and variety of services -- and the fact that it operates in a high-growth market -- the company could continue to post stellar growth. And that's why Shopify looks like a top long-term buy now.